I don't know if this will work for you but here's a trick I've used before.
dropbox.com/s/wyiz1r06s2p3o5w/autotile.c3p
The water is it's own layer under the tilemap, which is transparent where there should be water. It consists of two tiled backgrounds sliding across each other with the sine movements.
Alternatively, I imagine animating by swapping tiles should work perfectly well, if you constrain the updates to happen only if the tile is on screen, or animate only a random portion of the tiles at a time rather than all at once.