IOWA CITY — While Iowa City’s infamously tight rental housing market is growing with new apartment buildings, it likely won’t see gains in another type of housing — rental homes and duplexes near downtown. The Iowa City Council is set to vote Tuesday on the third and final consideration of rules to strengthen minimum rental housing requirements and effectively stop any increase in the number of rental homes and duplexes, stabilizing some of the most popular rental neighborhoods. The move is in direct response to a new state law passed earlier this year that said cities could no longer regulate the number of people living in a given unit based on their family status. The new law threw a wrench in how college towns like Iowa City legally could deal with teeming rentals — and the noise and traffic they can create — as students seek temporary places to live close to campus, including in established neighborhoods. “You’ve got this ecosystem that’s got a very delicate balance,” said Christopher Warnock, a member of the Goosetown Neighborhood Association, which is northeast of downtown.