Sounds like a loose spoke. Try tensioning up on the spokes if you have the tools and the know-how. Sometimes the relative motion that is caused by a loose spoke causes fretting on the spoke seats or where the spokes cross, and in this case it is too late and the spoke(s) will have to be replaced.
You can try squeezing together nearly parallel pair of spokes with your hands and you will usually (but not always) be able to recreate the clicking noise.