As long as the dish is 1 meter or less ( which will probably exclude most C band ), the homeowners association can screw themselves. Federal law supercedes any homeowners association agreements ( unless you live in a designated historic district). 47 CFR § 1.4000:
(a)(1) Any restriction, including but not limited to any state or local law or regulation ... or any private covenant, homeowners' association rule or similar restriction on property within the exclusive use or control of the antenna user where the user has a direct or indirect ownership interest in the property, that impairs the maintenance, installation, or use of ...
(i) an antenna that is designed to receive direct broadcast satellite service, including direct-to-home satellite services, that is one meter or less in diameter ...
(ii) an antenna that is designed to receive video programming services via multipoint distribution services ... and is one meter or less in diameter or diagonal measurement ...
(iii) an antenna that is designed to receive television broadcast signals; or
(iv) a mast supporting an antenna described in [the above paragraphs]; is prohibited to the extent it so impairs.
Yeah, even my six foot dish is considered marginal for C-band. Experimenters pull in some of the strongest C-band transponders with a 4 ft dish, but it is a chore, and unreliable in less than perfect weather. The closer to the equator you are, the smaller the dish you can get by with.