The record you found on RootsIreland seems to be a Civil birth record rather than a baptism, it turns up for me under a free search on Dunmore (CP), which is sub-district of Tuam registration district. The record transcript should probaly show a townland and narrow down the correct location. A cert from the GRO would show the complete details.
William's birth is the only one showing up for this couple on extracted records.
There seems to be two townlands named Co. Galway, one in Kilmoylan civil parish in Tuam PLU, and the other in Bullaun civil parish in Loughrea PLU, but I dont see any Keanes at either on the census returns ?
Shane