I am located in DownEast Maine. We do have a road association established for our private road. My question is this: if we have solicitors walking through the neighborhood and knocking on doors, do we have the right to ask them to leave because they are on our private road?

There are actually town ordinances where solicitors have to basically ask from the town permission to go door to door. Each town's process might be different. It appears if you put up a sign, no soliciting, also helps. Some towns have rules which offer enforcement if you use those signs for your home. Check with your town their policies. I don't think girl scout cookie season may apply.

There was a case where some young adults were going door to door offering some deal about CMP that was fake. What they were actually doing was looking inside your home from the doorway for any items they'd want to rob. It's sad to have to be so cautious these days.