1 shared car is shown to replace between 7 and 20 private cars in various deployments. Building new housing with dedicated car-share parking is a great way to go.
Maybe paid dedicated parking separate from the housing and only allowed to people that live in the area (with an increase in price for a second car for a household) would suffice, as long as it was planned well. But that's the problem, poor planning (or changes over time) could cause problems again.