Are you allowed to pray for your own death?

Question

No suicide or euthanasia is allowed in Judaism. But are you allowed to pray for your own death?

You can pray for the death of someone who is incurably sick, in pain and dying. This is based on Rabbenu Nissim's (14th century Spain) understanding of Nedarim 40a and Ketuvot 104a, ratified by the Aruch Hashulhan [YD 335:3] and Rabbi Feinstein [Igrot Moshe CM 2:74].

But I have not seen a responsum about whether someone is allowed to pray for his own death. Tanhuma implies that it's allowed, because that's what Moses did:

Moses said: Master of the universe, up to now I requested life, but now here is my soul given over to You. He had resigned himself to death... [Tanhuma on Deut. 31:2]

Answer 1

According to the Talmud (Shabbat 30a) King David asked to die (before his allotted time) and while God did not accept this request, there does not seem to be any mention that this was an inherently problematic request:

And as to what Solomon said, 'for a living dog is better than a dead lion', — that is as Rab Judah said in Rab's name, viz.; what is meant by the verse, Lord, make me to know mine end, and the measure of my days, what it is; let me know how frail I am. David said before the Holy One, blessed be He, 'Sovereign of the Universe! Lord, make me to know mine end.' 'It is a decree before Me,' replied He, 'that the end of a mortal is not made known.' 'And the measure of my days, what it is'-'it is a decree before Me that a person's span [of life] is not made known.' 'Let me know how frail [hadel] I am.' Said He to him. 'Thou wilt die on the Sabbath.' 'Let me die on the first day of the week!' 'The reign of thy son Solomon shall already have become due, and one reign may not overlap another even by a hairbreadth.' 'Then let me die on the eve of the Sabbath!' Said He, 'For a day in thy courts is better than a thousand': better is to Me the one day that thou sittest and engagest in learning than the thousand burnt-offerings which thy son Solomon is destined to sacrifice before Me on the altar.'

(Soncino translation, my emphasis)

Answer 2

Ever so fitting, Jonah (Iyov) prayed for his death two times in the course of his ordeals.

Chapter 4:

And he prayed to G‑d, and said: "I pray thee, O G‑d, was not this my saying, when I was still in my own country? Therefore I fled beforehand to Tarshish; for I knew that You are a gracious G‑d, and merciful, slow to anger, and great in love and repentest of the evil. Therefore now, O G‑d, take my life from me, I pray thee; for it is better for me to die than to live." And G‑d said: "Are you so greatly vexed?" Then G‑d appointed a worm when the dawn came up the next day, and it attacked the plant, so that it withered. And it came to pass, when the sun arose, that G‑d prepared a vehement east wind, and the sun beat down upon the head of Jonah, so that he fainted; so he asked that he might die, and he said: It is better for me to die than to live.

[...]

And G‑d said to Jonah: "Are you so greatly vexed on account of the plant?" And he said: "I am greatly vexed to death"

I conclude that you are you are clearly allowed to pray for your own death. I reckon you are allowed to pray for absolutely anything. Whether your prayers get answered in the way you imagine or hope for is an entire different thing.