The prayers of Vṛtrāsura appear in the Śrīmad Bhāgavatam SB 6.11.22–27. We present Babaji’s translations below.

पुंसां किलैकान्तधियां स्वकानां या: सम्पदो दिवि भूमौ रसायाम्
न राति यद्‌द्वेष उद्वेग आधि र्मद: कलिर्व्यसनं सम्प्रयास:

puṁsāṁ kilaikānta-dhiyāṁ svakānāṁ
yāḥ sampado divi bhūmau rasāyām
na rāti yad dveṣa udvega ādhir
madaḥ kalir vyasanaṁ samprayāsaḥ

Bhagavān does not give heavenly, earthly, or subterranean wealth to His
devotees whose hearts belong to Him alone, lest that wealth become the cause
of hatred, anxiety, mental agitation, pride, quarrel, adversity, or great endeavor.

त्रैवर्गिकायासविघातमस्मत्-पतिर्विधत्ते पुरुषस्य शक्र
ततोऽनुमेयो भगवत्प्रसादो यो दुर्लभोऽकिञ्चनगोचरोऽन्यै:

trai-vargikāyāsa-vighātam asmatpatir
vidhatte puruṣasya śakra
tato ’numeyo bhagavat-prasādo
yo durlabho ’kiñcana-gocaro ’nyaiḥ

O Indra! If a devotee strives for artha, dharma, and kāma, our Master obstructs
these endeavors. Such obstructions are signs of His compassion, which nondevotees
rarely obtain. It is attained only by those who have taken complete
shelter of Him.

अहं हरे तव पादैकमूल दासानुदासो भवितास्मि भूय:
मन: स्मरेतासुपतेर्गुणांस्ते गृणीत वाक् कर्म करोतु काय:

ahaṁ hare tava pādaika-mūladāsānudāso
bhavitāsmi bhūyaḥ
manaḥ smaretāsu-pater guṇāṁs te
gṛṇīta vāk karma karotu kāyaḥ

O Śrī Hari, please be gracious on me so that in my next life I again receive the
opportunity to serve the servants who take exclusive shelter of Your lotus feet.
O Master of my life, may my mind always remember Your auspicious qualities;
may my words always recite them; and may my body always engage in Your
service.

न नाकपृष्ठं न च पारमेष्ठ्यं न सार्वभौमं न रसाधिपत्यम्
न योगसिद्धीरपुनर्भवं वा समञ्जस त्वा विरहय्य काङ्‌क्षे 

na nāka-pṛṣṭhaṁ na ca pārameṣṭhyaṁ
na sārva-bhaumaṁ na rasādhipatyam
na yoga-siddhīr apunar-bhavaṁ vā
samañjasa tvā virahayya kāṅkṣe

O Ocean of all good fortune, I do not desire anything that is devoid of service
to You; neither residence in heaven, nor in Satyaloka, nor kingship over the
whole earth, nor sovereignty over the lower regions, nor any of the yogic
perfections. I do not want even liberation.

अजातपक्षा इव मातरं खगा: स्तन्यं यथा वत्सतरा: क्षुधार्ता:
प्रियं प्रियेव व्युषितं विषण्णा मनोऽरविन्दाक्ष दिद‍ृक्षते त्वाम्

ajāta-pakṣā iva mātaraṁ khagāḥ
stanyaṁ yathā vatsatarāḥ kṣudh-ārtāḥ
priyaṁ priyeva vyuṣitaṁ viṣaṇṇā
mano ’ravindākṣa didṛkṣate tvām

Hatchlings eagerly wait for their mother to bring them food. Hungry calves
anxiously hanker for the milk from their mother’s udder. A loving wife
earnestly waits for the return of her husband from a foreign land. O Lotus-eyed
Lord, my mind desires to see You with the same intense feeling.

ममोत्तमश्लोकजनेषु सख्यं संसारचक्रे भ्रमत: स्वकर्मभि:
त्वन्माययात्मात्मजदारगेहे-ष्वासक्तचित्तस्य न नाथ भूयात्

mamottamaśloka-janeṣu sakhyaṁ
saṁsāra-cakre bhramataḥ sva-karmabhiḥ
tvan-māyayātmātmaja-dāra-geheṣv
āsakta-cittasya na nātha bhūyāt

O Bhagavān, I do not desire liberation. I do not mind if my karma requires that
I take many more births, but I pray that whatever species I may be born into, I
may be friendly with Your devotees. O Master, I pray not to have any relations
with people who are attached to their bodies, children, spouses, and homes,
under the influence of Your māyā.