Suicide in Islam
Question

I have a cousin (the daughter of my maternal aunt) who died, and it seems most likely that she committed suicide. What is the ruling on one who commits suicide? What is his position before his Lord? What can her parents do to reduce her punishment?
Praise be to Allah.The Seriousness of Suicide in Islam
Suicide is a major sin in Islam . The Prophet (peace and blessings of Allah be upon him) stated that the one who commits suicide will be punished with something like that with which he killed himself. 
Abu Hurayrah (may Allah be pleased with him) narrated that the Prophet (peace and blessings of Allah be upon him) said: “Whoever throws himself down from a mountain and kills himself will be in the Fire of Hell, throwing himself down therein for ever and ever. Whoever takes poison and kills himself, his poison will be in his hand and he will be sipping it in the Fire of Hell for ever and ever. Whoever kills himself with a piece of iron, that piece of iron will be in his hand and he will be stabbing himself in the stomach with it in the Fire of Hell, forever and ever.” (Narrated by Al-Bukhari, 5442; Muslim, 109) 
It was narrated from Thabit ibn Ad-Dahhak (may Allah be pleased with him) that the Messenger of Allah (peace and blessings of Allah be upon him) said: “Whoever kills himself with something in this world will be punished with it on the Day of Resurrection.” (Narrated by Al-Bukhari, 5700 and Muslim, 110) 
It was narrated that Jundub ibn `Abdullah (may Allah be pleased with him) said: The Messenger of Allah (peace and blessings of Allah be upon him) said: “Among those who came before you there was a man who was wounded and he panicked, so he took a knife and cut his hand with it, and the blood did not stop flowing until he died. Allah said: ‘My slave hastened to bring about his demise; I have forbidden Paradise to him.” (Narrated by Al-Bukhari, 3276; Muslim, 113.)
Can you offer Janazah prayer for one who commits suicide?
The Prophet (peace and blessings of Allah be upon him) refrained from offering the funeral prayer for one who had committed suicide , as a punishment to him and so as to deter others from doing what he had done. But he gave the people permission to offer the funeral prayer for him, so it is Sunnah for the people of knowledge and virtue not to offer the funeral prayer for one who has committed suicide , following the example of the Prophet (peace and blessings of Allah be upon him). 
It was narrated that Jabir ibn Samurah (may Allah be pleased with him) said: A man who had killed himself with a broad arrow-head was brought to the Prophet (peace and blessings of Allah be upon him) and he did not offer the funeral prayer for him. (Narrated by Muslim, 978) 
This Hadith is evidence for those who say that the funeral prayer should not be offered for one who killed himself because of his sin. This is the view of `Umar ibn `Abd Al-`Aziz and Al-Awza`i. But Al-Hasan, An-Nakha`i, Qatadah, Malik, Abu Hanifah, Ash-Shafi`i and the majority of scholars said that the funeral prayer should be offered for him. They responded to this Hadith by pointing out that the Prophet (peace and blessings of Allah be upon him) did not offer the funeral prayer for him himself so as to deter the people from doing something similar, but the Companions offered the funeral prayer for him.  (Sharh Muslim, 7/47)
Is suicide Kufr (disbelief)?
This does not mean – if it is proven that your cousin did commit suicide – that you should not pray for mercy and forgiveness for her, rather you must do that because she needs that. Suicide is not Kufr that puts a person beyond the pale of Islam as some people think, rather it is a major sin that is subject to the will of Allah on the Day of Resurrection: if He wills, He will forgive it, and if He wills He will punish for it. So do not neglect to make Du`a for her and be sincere in doing so; perhaps that may be the means of Allah forgiving her.  
And Allah knows best.