I would think one of the best sources is actually going to be the church records.. I have alot of the church records on my machine (they are available on microfilm at LDS libaries).. and since you have a specific townland (Rhue/ Rue) i am willing to do a lookup.. i just need a general timeframe ... and clarification on whether Mary Walsh's birth name is really Walsh..
The Thomas Walsh's from Rhue that i have recorded..
Thomas Walsh 1880 child of Matthew Walsh and Bridget Brennane
Thomas Walsh 1861 child of Pat Walsh and Mary Higgins
Thomas Walsh 1856 child of Thomas Walsh and Anne Stenson
But there might be some more that i just have not looked up yet..
I do have some distant connections to the Walsh line via my Price and Kilcoyne surnames.. which is why i have looked some of these up..