If you rent to someone against the rules of your HOA, without some waiver or consent from the HOA, they could take various legal actions, including seeking monetary compensantion from you or seeking a court order preventing the rental. HOA rules are legaly enforceable; review the HOA documents to see what they say will happen in this case.If you ask for permission and they refuse, you do not have any options; unless the HOA documents compel them to "not unreasonably withhold" approval, they have the right to say "no" for any reason, without justifying it.