Van islamqa:
The Prophet (peace and blessings of Allaah 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 Allaah be upon him).
It was narrated that Jaabir ibn Samurah (may Allaah have mercy on him) said: A man who had killed himself with a broad arrow-head was brought to the Prophet (peace and blessings of Allaah be upon him) and he did not offer the funeral prayer for him. Narrated by Muslim, 978.
This hadeeth 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-‘Azeez and al-Awzaa’i. But al-Hasan, al-Nakha’i, Qataadah, Maalik, Abu Haneefah, al-Shaafa’i and the majority of scholars said that the funeral prayer should be offered for him. They responded to this hadeeth by pointing out that the Prophet (peace and blessings of Allaah be upon him) did not offer the funeral prayer for him himself so as to deter the people from doing something similar, but the Sahaabah offered the funeral prayer for him. End quote.
Sharh Muslim, 7/47
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 Allaah 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’aa’ for her and be sincere in doing so; perhaps that may be the means of Allaah forgiving her.
And Allaah knows best.