"When I Go" (Dave Carter) has become something of a traditional choice when mourning filkers. I'd certainly like it for my own funeral. ("Julian of Norwich" is also a common choice but I don't myself think of it as a funeral song.)

Among more classical choices, I've always liked Albinoni's "Adagio in G minor".

I could probably think of more if I put my mind to it. Maybe I should, I'm turning 40 in two days. Death is near! :-)