the mayor is on the council
Commonly, in the UK a councellor is said to be ON the council, ie a member of it. In the council would mean physically present in the venue.
Each is acceptable here, in my opinion.
A quick search for "ar an gcomhairle" turns up quite a few hits, which suggests that "sa chomairle" and "ar an gcomhairle" may have the same two different meanings in Irish that they do in English - in the council and on the council.