The Irish Family History Research Center listing for Co Clare is:
Clare Heritage Centre
[this is their mailing address]
International phone +353-65-37955
Contact: Antoinette O'Brien
Co. Clare site has no web page or fax no listing.
These centers will research their data base for a fee.
I contacted the Limerick Regional Archives, The Granay, Michael Street, Limerick City. Phone (061) 410777, International phone
+353 61 410777, Contact Dr. Chris O'Mahony. Limerick web site http://www.mayo-Ireland.ie
This site brings up form and instructions to send $50 for initial search. I understand responses may take several months.
Clare does not have a web page, but their procedure is probably similar to Limerick. If you have specific dates, townland and parish, this aids their search. Obviously, McMahon is a common name in Co. Clare, so the more specific your informaion, the more likely they can identify birth, death and marriage records for your people.