A song sung at a burial

One word substitute is Dirge.

Elegy: (in modern literature) a poem of serious reflection, typically a lament for the dead.
Ode: a lyric poem, typically one in the form of an address to a particular subject, written in varied or irregular metre.
Dirge: a mournful song, piece of music, or sound.
Ballad: a poem or song narrating a story in short stanzas. Traditional ballads are typically of unknown authorship, having been passed on orally from one generation to the next.