Some devotees claim that Sriman Nityananda Prabhu and Sri Advaita Acarya can only “bestow general bhakti” (what is that actually?) and that they have “no role in Vraja-lila”.

We simply cannot agree.

First of all, Srila Narottama das Thakur sings:

heno nitāi bine bhāi, rādhā-kṛṣṇa pāite nāi

“Unless one takes shelter under the shade of the lotus feet of Lord Nityananda, it will be IMPOSSIBLE to attain Radha-Krsna.”

Why is it impossible?

Nityananda Prabhu is giving us Gaura-prema, love for Gauranga. For us, Gauranga is Radhika, so giving away Gaura-prema means distributing love for Srimati Radhika, meaning giving away prema in manjari-bhava, serving the Divine Couple as a beloved maidservant.
Sriman Mahaprabhu appeared to distribute EXACTLY this kind of love.

anarpita-carim cirat karunayavatirnah kalau
samarpayitum unnatojjvala-rasam sva-bhakti-sriyam
harih purata-sundara-dyuti-kadamba-sandipitah
sada hridaya-kandare sphuratu vah saci-nandanah

May the Supreme Lord who is known as the son of Srimati Saci-devi
be transcendentally situated in the innermost chambers of your heart.
Resplendent with the radiance of molten gold,
He has appeared in the Age of Kali by His causeless mercy to bestow
what no incarnation has ever offered before:
the most sublime and radiant mellow of devotional service, the mellow of conjugal love.

So, if we can´t attain the mercy of Sri Caitanya Mahaprabhu without the mercy of Sriman Nityananda Prabhu, how is it possible that Nityananda Prabhu “can” only give “general” bhakti as some devotees claim.
unnatojjvala-rasam sva-bhakti-sriyam – this is NOT general bhakti, but the HIGHEST bhakti. It is the love in the hearts of the Vraja-sundaris, the maidservants of Srimati Radhika. Sriman Mahaprabhu came to give us nothing more and nothing less.

So without the mercy of Sri Nityananda Prabhu, we can´t attain the mercy and love for Sriman Mahaprabhu…and without the mercy of Sriman Mahaprabhu we can´t attain the gift He had come to give: MANJARI-BHAVA…

Ergo, the mercy of Sri Nityananda is very important for attaining the goal of life, manjari-bhava.
Sriman Mahaprabhu is unnatojjvala-prema Himself, and He came to give us this “unnatojjvala rasam sva-bhakti-sriyam” (the wonderful service to Srimati Radhika as Her manjari).
Nityananda Prabhu is the personification of Caitanya Mahaprabhu’s most magnanimous mercy.

ye bhakti gopikā-gaṇer kabe bhāgavate 
nityānanda hoite tāhā pāila jagate

“The love for Krishna in the mood of the gopis which is described in the Bhagavata is attained in the world through Nityananda.” 
(Caitanya Bhagavata, 3.5.303)

Mahaprabhu tells Raghava Pandit:
“I tell you confidentially that Nityananda is completely non-different from me.” 
(Caitanya Bhagavata, 3.5.100-104)

nityananda namas tubhyam premananda-pradayine
kalau kalmasha-nasaya jahnava-pataye namah
Sri Stava-kalpa-druma

“I offer pranama unto Sri Nityananda Prabhu who bestows the bliss of divine love, who
eliminates the contamination of the age of Kali, and who is the master of Jahnava-devi.”

caitanyera adi-bhakta nityananda-raya
caitanyera yaso vaise yanhara jihvaya
ahar nisa caitanyera katha prabhu kaya
tan’re bhajile se caitanye bhakti haya
CB Adi 9.217-218

Lord Caitanya’s first and foremost devotee is Nityananda Raya. The glories of
Lord Caitanya are always on his tongue. Day and night Lord Nityananda speaks only of Lord Caitanya. Whoever worships Him is a real devotee of Sri Caitanya. Nityananda is the gateway through which all service to Lord Caitanya must pass.

nityananda avadhuta sabate agala
caitanyera dasya-preme ha-ila pagala
CC Adi 6.48

Nityananda, the wandering mendicant, is the foremost of all the servants of
Lord Caitanya. He is like the gateway through which all service to Lord Caitanya must pass. He became mad in the ecstasy of service to Lord Caitanya.

preme matta nityananda kripa-avatara
uttama, adhama, kichu na kare vicara
ye age padaye, tare karaye nistara
ataeva nistarila mo-hena duracara
CC Adi 5.208-9

Nityananda is intoxicated by ecstatic love and is an incarnation of mercy, He
makes no distinction between the exalted and the fallen. He delivers all those who fall down before Him. Therefore He has delivered such a sinful and fallen person as me.

dui bhai eka-tanu samana-prakasa
nityananda na mane, tomara habe sarva-nasa
ekete visvasa, anye na kara sammana
“ardha-kukkuti-nyaya” tomara pramana
CC Adi 5.175-176

These two brothers (Gaura and Nitai) are like one body; they are identical manifestations. If you do not believe in Lord Nityananda, you will fall down. If you have faith in one, but disrespect the other, your logic is like the logic of accepting half a hen.

sri-caitanya – sei krishna, nityananda – rama
nityananda purna kare caitanyera kama
CC Adi 5.157

Lord Caitanya is the same Lord Krishna, and Lord Nityananda is Lord Balarama. Lord Nityananda fulfills all of Lord Caitanya’s desires.

jaya jaya nityananda, nityananda-rama
yanhara kripate painu vrindavana-dhama
jaya jaya nityananda, jaya kripa-maya
yanha haite painu rupa-sanatanasraya
yanha haite painu raghunatha-mahasaya
yanha haite painu sri-svarupa-asraya
sanatana-kripaya painu bhaktira siddhanta
sri-rupa-kripaya painu bhakti-rasa-pranta
jaya jaya nityananda-caranaravinda
yanha haite painu sri-radha-govinda
CC Adi. 5.200-204

All glory, all glory to Lord Nityananda Balarama, by whose mercy I have
attained shelter in the transcendental abode of Vrindavana. All glory, all glory to the merciful Lord Nityananda, by whose mercy I have attained shelter of Sri Rupa and Sanatana. By His mercy, I have attained the shelter of the great Sri Raghunatha dasa Gosvami, and by His mercy I have found the refuge of Sri Svarupa Damodara. By the mercy of Sanatana Gosvami I have learned the final conclusions of devotional service, and by the grace of Sri Rupa Gosvami I have tasted the highest nectar of devotional service. All glory, all glory to the lotus feet of Lord Nityananda, by whose mercy I have attained Sri Radha-Govinda.

As far as the role of Sri Advaita Acarya is concerned:

advaita acarya, nityananda, dui anga
duijana lana prabhura yata kichu ranga
CC Adi 5.146

Nityananda Prabhu and Advaita Acarya are the two expansions of Lord
Caitanya Mahaprabhu who assist His transcendental pleasure-pastimes.

eka mahaprabhu, ara prabhu duijana
dui prabhu sebe mahaprabhura carana
CC Adi 7.14

There is one mahaprabhu and two prabhus. The two Prabhus serve the lotus feet of Mahaprabhu.

sei navadvipe vaise vaishnavagraganya
‘advaita acarya’ nama, sarva-loke dhanya
jnana-bhakti-vairagyera guru mukhyatara
krishna-bhakti vakhanite ye hena sankara
CB Adi 2.78-9

Residing in Navadvipa at that time was Sri Advaita Acarya, the topmost Vaishnava, who is glorified throughout the world. Sri Advaita Acarya was the chief amongst the Gurus in knowledge, devotion and renunciation. He was as expert as Lord Siva in explaining the devotional service of Lord Krishna with knowledge and renunciation.

maha-vishnura amsa advaita guna-dhama
isvare abheda, teni ‘advaita’ purna nama
CC Adi 6.26

Sri Advaita, who is the reservoir of virtues, is the main limb of Maha-Vishnu. His full name is therefore Advaita, for He is identical in all respects with the Lord.

jiva nistarila krishna-bhakti kari’ dana
gita-bhagavate kaila bhaktira vyakhyana
CC Adi 6.28

He delivered all living beings by offering the gift of krishna-bhakti. He explained Bhagavad-Gita and Srimad-Bhagavatam in the light of devotional service.

So clearly Sri Advaita Acarya is not only there for “giving general bakti”. He was the One Who called down Sriman Mahaprabhu to bestow pure prema to the world.

As far as the roles in Vraja-lila is concerned:
One verse already precisely explained that Sriman Nityananda Prabhu is nobody else but Sri Balarama.
In a more esoteric truth, He is also Srimati Radhika´s younger sister, Ananga Manjari.

Advaita Acarya is also fully present in Vraja-lila.
My good friend Advaita das wrote this on his homepage (www.madangopal.com):

All parshadas (associates) of Sri Caitanya Mahaprabhu have a svarupa in madhura rasa. Advaita Prabhu is Visakha and Rati Manjari.
All lines descending from  Mahaprabhu’s parshadas can bestow gopi-bhava and gopi-prema. Though they may be famous as personalities in Vraja outside of gopi-bhava (f.i. Nityananda is Balarama but also Ananga Manjari), they all have a place in gopi-bhava as well. When Rupa Gosvami had completed his recitation of his dramas to Mahaprabhu and His associates at Siddha Bokul in Puri, Mahaprabhu asked for the blessings of Nityananda and Advaita Prabhu upon him, which They bestowed – advaita nityanandadi sab bhaktagan; kripa kori rupe sobe koila alingan (CC Antya 1.207).
“Advaita Ācārya, Nityānanda Prabhu and all the other devotees showed their causeless mercy to Rūpa Gosvāmī by embracing him in return.
That would have been pointless and powerless unless they themselves had the power of gopi-bhava within them.

Sri Murari Gupta eulogises Advaita Prabhu in the introduction of his Sri Krishna Caitanya Carita Maha-kavya (1.20):

sri-yuktadvaita-varyah parama-rasa-kalacarya iso vireje
“The most glorious Advaita is the Supreme Lord and the greatest teacher of the
highest rasa, the divine amorous flavour.”
(http://madangopal.com/advaitadefense.pdf)

So ALL parshadas of Sriman Mahaprabhu can bestow gopi-bhava/gopi-prema.