This question can be done by visualisation only.
For A, all forces on q are pushing it towards the centre(all are repulsive in nature).So it is bound to go back to the centre.
For B, say you displace it a bit towards right, then the forces pulling it towards right are stronger than those pulling towards left(due to lesser distance from right). And this difference will keep on increasing throughout, so the charge will hit the ring 100%.
For C, there's always a restoring force on the charge towards centre, so it will perform SHM.
Since option A is correct(q tends to come back to the centre), the charge is in stable equilibrium, thus, option D is incorrect.