Gosh each of those maiden names for Mary are illegible (or is that just how they are showing up on this forum ).
I'm not sure what you know of Irish records but our civil registration only began in 1864 so prior to that you are looking for church records ~ this pretty much leaves you with just rootsireland as the only real option.
rootsireland is a great site BUT you need to know how to use it properly.
When / If you know an EXACT parish that your family came from you are best of to first check if records from the period you are researching even exist.
IF they do exist then you should do your searches through that exact parish (rootsireland have this option).
Also, use the surname variations sheets that rootsireland have.
For example with Mary there are a LOT of variations for her surname on rootsireland's spreadsheet so what I tend to do is on a seperate piece of paper, write all the viable options down, and then go in and do my searches that way.
So, just to sum up, I think the marriage that I sent you is a very good possibility BUT with the little bit of information you have to go on it will be near on impossible to ever be 100% sure.
I'm afraid that's the nature of looking for nearly 200 year old Irish records

Tara