A slotted ring that allows simultaneous transmissions of messages by different users is considered. Such a ring network is commonly called ring with spatial resue. It can achieve significantly higher throughtput than standard token rings but it also can lead to unfairness problems. Policies that operate in cycles and quarantee that a certain number (quota) of packets will be transmitted by every node in every cycle have been considered before to alleviate the unfairness. We consider here the problem of designing a policy that will result in a stable system whenever the arrival rates are whitin the stability region of a ring with spatial reuse (the stability region is defined as the set of node arrival rates for which there is a policy that makes the ring stable). We provide such a policy. No knowledge of arrival rates or message destination probabilities are required. The policy is an adaptive version of the quota policies and can be implemented with the same distributed mechanism. We shall use Lyapunov test function techniques together with the regenerative approach to derive our main results.