Weird as it may sound, but a funeral can also be a time for rejoicing. This, in some ways, is the celebration of being born into Eternal Life in some religions - Ok, Flight of the Bumblebee would be quite inappropriate (unless specifically requested), but everything does not have to be in a minor key and played so painfully slow - That will put people to sleep.
Handel's Water Music Suite for Organ works well, as does the Pachelbel Canon in D. Jesu, Joy of Mans' Desiring, hymns like Beautiful Saviour, Rock of Ages, What a Friend, Amazing Grace, How Great Thou Art, (etc)are all ones that I use at funerals here. Of course, I do my own improvs of each of those hymns during which I will employ elaborate key changes and registration changes. And I don't limit my funeral prelude to just the softest flues either - I open it up and let 'er rip a few times too - nothing sacreligious about that whatsoever.
Soothing music works too ... but for me, it's too Funeral Parlor"ish" ... and depressing.