Dear Jane
Welcome to Ireland Reaching Out and apologies for the delay in replying to your message.
As you can see from the link below, Newmarket is a townland in the Civil Parish of Tomfinlough:
http://www.irishtimes.com/ancestor/fuses/townlands/index.cfm?fuseaction=TownlandsInCivil&civilparishid=2786&civilparish=Tomfinlough&citycounty=Clare
Records for the corresponding Roman Catholic Parish of Newmarket begin in 1828. Bunratty is also a Civil Parish in Co. Clare. The corresponding Roman Catholic Parish is Newmarket also.
http://www.irishtimes.com/ancestor/fuses/townlands/index.cfm?fuseaction=TownlandsInCivil&civilparishid=2713&civilparish=Bunratty&citycounty=Clare
You could check the sites below for information about the family:
www.familysearch.org has a huge database of genealogical records including some church records for Ireland.
www.rootsireland.ie have a large collection of Irish Church records, however you have to pay to use this site.
http://churchrecords.irishgenealogy.ie/churchrecords/ have begun a project to upload Irish church records to their site free of charge. However so far only Counties Dublin, Kerry, Carlow and parts of Cork have been covered.
Another website that may be helpful is:
Clare Local Studies Centre: http://www.clarelibrary.ie/eolas/library/local-studies/locstudi1.htm&nb…;
Remember to post any new information that you find here. The more information you post, the more likely it is that one of our volunteers will be able to advise or assist you. Also include information concerning which sources you may have already used so others may further your search.
Best of luck with your search
Clare Doyle
Genealogy Support