Cloy: to become uninteresting or distasteful through overabundance; to cause distaste or disgust by supplying with too much of something originally pleasant; sate, satiate, surfeit.
"The Christians of old...
However employed their joy was the same;
They never were cloyed in hymning the Lamb;
Their sole recreation - to sing of His praise,
And publish salvation by Jesus' grace." -- # 206, From The Primitive Hymns, Spiritual Songs and Sacred Poems, by Benjamin Lloyd, 1841/ The Primitive Hymn Corp., 1999
Martha Henderson wrote of a service (not Sacred Harp) in which she encountered songs that "were so saccharine and so relentlessly cheerful that they were cloying." -- as quoted by Kiri Miller in A Long Time Traveling