If the councillor has actually resigned in writing to the chairman (the correct procedure for resignation by a councillor who is not the chairman) then he has ceased to be a councillor. If he has only announced his resignation, then he is still a councillor and can change his mind.
If he is no longer a councillor, there is no alternative to going through the process for a casual vacancy, which gives the electorate the option to demand a poll. Assuming that is not exercised, then the council will be free to co-opt the former councillor. I could be wrong, but in the circumstances, I don't think there is an obligation to consider alternative candidates if the council does support the individual who resigned.
If a poll is demanded, it is all down to who submits a valid nomination, and who the electorate choose (if there is more than one valid nomination).