Pretty much any moss will grow on it as long as the humidity is in the high 70's or above. You can just place the java moss on it, leaving a few strands to venture into the water and it will eventually take over the wood. You could also use a tropical, terrestrial moss. Heck, you can even go find a stream and field collect some moss from some rocks and use that if you prepare it properly.

As far as ferns, they will grow on the log and you don't even need to root them in anything. A majority of ferns are epiphytic by nature. Just place some rehydrated long fiber sphagnum moss around the roots and you're good to go. Black jungle sells an azolla fern which normally is a floater (looks a bit like duckweed), but will grow up onto the wood and take it over.

Your options are many. It just depends on your taste.