Midway (midwayusa.com) sells picatinny rails made by Badger Ordnance that will fit the remmy action. They are not cheap, about $145, but are good. I have them on three different rifles. I don't know about the rimfire though, Badger may make one??? Midway also has Badger Ordnance rings.
Night Force also makes Picatinny rails and rings of excellent quality. Check with Dan Lilja at Lilja Precision rifle barrels (www.riflebarrels.com