No European state that'd be eligible has chosen to voluntarily stay outside. Azerbaijan and Russia are the closest to being in trouble of the current members (Russias voting rights were suspended over the annexation of Crimea; Azerbaijan is implicated in corruption to step criticism over Aliyev's rule).
The "European states outside the CoE club" is not exactly one to strive for membership of, to the extent even a lot of Tory MPs in favour of Brexit are opposed to leave the ECHR; David Davis in fact threatened to rebel over it at one point.