See thread Water Kelpie/Oran Tlaidh an Eich-Uisge. Relates mostly to water-horse songs from Skye, but mentions also the Manx tune, making the point that Arrane Ghelby may well refer not to a Kelpie at all, but to Dalby, the place where the melody was heard. Certainly, the story told with the tune was of an old old man in a boat, and later attempts by folklorists to identify him as a kelpie in human form strike me as rather contrived.

On the whole, folk-beliefs of this sort don't turn up much in traditional song (the Annan Water example has the air of literary intervention). I don't know why, but it may in part be because such beliefs tend to be local, and in order to spread more widely songs need a general appeal. The surviving songs which do mention the water-horse (or which appear to) are usually lullabyes, found only locally.

There may perhaps be a better stock of material to be found in the Scandinavian countries.