Instead of seeking perfect stability against group deviations (which often doesn't exist), you can compute equilibria that minimize coalition incentives to deviate—and these are guaranteed to exist and computable in reasonable time.
This paper introduces a new equilibrium concept that minimizes how much coalitions can gain by deviating together, rather than requiring such deviations to be impossible (which rarely happens). The authors provide algorithms to compute these equilibria efficiently and connect the framework to finding the best social welfare achievable with bounded vulnerability to single-player exploits.