I need songs that express deep emotions, and are sung with emotions of grieving.
Are you asking for a list that has already been compiled, or are you asking for suggestions of specific songs in order to create such a list?
By “Christian songs”, do you mean hymns or contemporary Christian popular music or any kind of music that is identifiably Christian?
Some hymnals are organized topically, and may have sections on mourning, grief, or loss.
https://churchleaders.com/worship/worship-articles/175185-kristen-gilles-40-songs-for-grieving.html
This is a link to some decent contemporary Christian songs.
I would only recommend music like that of Bach for this purpose.