This might be tricky. The births are all before statutory registration and so you won?t get a statutory marriage certificate for this couple. You need to rely on church records instead but unfortunately a lot of RC parishes don?t have records as far back as 1825 - 1836. For example, the earliest RC records for Loughguile start in 1845, Ballintoy's in 1872, so if that?s where the family originated, there are no records to look up.
Perhaps someone may have information on the family from family sources, but otherwise it could be difficult.
You can see what RC records exist for Co Antrim, and where copies are kept, using this link:
http://www.irishtimes.com/ancestor/browse/counties/rcmaps/antrimrc.htm
The 1901 census has 137 people of the name McMichael in Co Antrim. 45 were RC; 55 were Presbyterian; 18 Methodists, 8 Church of Ireland, 7 Baptists. Don?t know if that helps you decide which denomination yours were.