Dear Paul:
Welcome to Ireland Reaching Out. Unfortunately, the Mountshannon parish registers only begin in 1846, so there is probably not a baptism reference for Catherine Mary, although there might be references for younger siblings if they existed. You might also note that the surname Mannix was also synonomous with the surname Minogue and this is important to note for any research.
I did not find a reference to a Dennis Mannix in Mountshannon, but I did find a reference to a Dennis Minogue there from the townland of Middleline South. This reference is to a holding which is transcribed on the website Clare Library. Here is the link for your reference:
http://www.clarelibrary.ie/eolas/coclare/genealogy/griffiths/griffithm9.htm
There is also a Dennis Minogue in Scariff (civil parish of Moynoe) living in the townland of Meenross. His reference is on the same link.
Both men had families.
Denis Minogue of Mountshannon had a daughter, Winifred baptised 3 June 1847. Her mother's name was Winifred Goonane (Guinane). There do not appear to be other children listed on the parish register for this family, but that is not conclusive to say that there weren't other children.
Denis Minogue of Scariff had children with Catherine Dwyer. It is not clear that this Denis resided in Meenross as the townland is not given.
Another Denis Minogue of Scariff had children with Mary (Maria) Nash. This family resided in Clonusker.
If you have other sibling's names for Catherine Mary Mannix, they might assist to narrow down which family she was connected with.
Not to further confuse you, but prior to about 1898, Mountshannon parish was also in part of County Galway, so you may need to look there as well.
Please get back to me with any questions, as there are several Mountshannon historians who may be able to assist.
Happy New Year!
All the best,
Jane