Rabbitt dilemna

Hi, I have 3rd great grandparents that I am trying to figure out who their parents are. William and Catherine Rabbitt. They were in Ballingarry, Kilchreest, Loughrea, Galway, How can I get further back? I think I have a lead on a few people who I think are siblings but it's hard to figure just how to find out the parents? Any suggestions?? William was born in 1805. I can't seem to find his death record. Any suggestions there??

Thanks, babsbunny