Josie:
Welcome to ireland Reaching Out!
In the mid-19th century, Houlihan was found mainly in Clare, Cork and Tipperary but there were many variant spellings. This Irish Times web site will show you how the surname was distributed and the various variant spellings.
http://www.irishtimes.com/ancestor/surname/
Civil registration started in 1864 so only church records if they are available would be your best source. However, you really need to know Michael's parents names to try to find a record and know you have the right record. Do you have Michael's death record or some other source which might show his parents names?
Roger McDonnell