Don't try painting over them. Paint is paint, and unless you can remove it, you'll just end up making the paint spot bigger. (Besides, most rock isn't a uniform color; it has gradations and imperfections - even a close match will stick out because it's a solid block of uniform color.)

Sounds like a good Eagle Scout project - contact your local Scout troops and find out if they've got kids looking for projects. They might be able to organize an effort, research removal methods, and get some volunteers to help.

Be glad it's paint. Where I hike, there are some sandstone cliffs where the local idiots use knives and chisels to carve their inanities - impossible to remove without doing even more damage.