You can place restrictions on renting units, but you might want to try some other strategies first.
When community associations start discussing what they should do about renters, it is often because of a horror story. In the last several years, I have helped associations deal with renters whose alleged activities have included loud parties; fights and disturbances; child abuse; strange people coming and going at all hours of the day and night; drug dealing; prostitution (both male and female); car break-ins and apartment burglaries; vandalism and other abuses of property; harassment and assault of managers, board members, owners, and other tenants; and every other conceivable social ill. While these kinds of activities sometimes involve owners, usually the perception is that renters are problems.