While waiting for replies to this post, use the Galway telephone book to find people to write too.
Bullaun was a Parish and a townland in the Union areas of Loughrea, Tuam and Gort.
The phone book is a bit strange as it lists along with the Keane's every person with K for a first and last name, by the time you pare that down you end up with 8 Keane's in the Loughrea area. Pick a male name and write. You can print up a covering letter and a family tree on the reverse
and photocopy them. Its worth a try and stamps are relatively inexpensive.
If you are looking back further than the family there are a number of websites available to you.