Thank you for your post to the Ireland Reaching Out message board. Sr deLourdes is the person that you will want to contact as she is extremely knowledgeable about the Gort area. I did find a 1901 Census record for a Cunnare family in the Gort area and the link is here: http://www.census.nationalarchives.ie/pages/1901/Galway/Gort/Lavally/1383861/
I'm not sure if this family was connected to your ancestors, and I will leave that Sr for her expertise. You should hear from her in the next week or so.
Thank you for your interest in the Ireland Reaching Out programme.