Hi Addys & Miriam, firstly I am not really any further ahead than Miriam, while you did not ask I located Catherine Tobins birth copy attached below but it is on the site I previously posted. I had hoped they might be neighbours. Catherine's mothers name is Meade living in Meath. Birth registered in Drogheda.
The only marriage that comes close is the one Miriam found, I had hoped your Thomas's father was christened one name but used his 2nd name to avoid confusion with others in the family, but the only likely Philip did not have a father Peter, born Drogheda in 1840, I am using the site Roots Ireland which is good for BMD pre 1864, I have been told that it is possible to join for a day which might assist you, it is not like other subscription sites where you join and search, if you join to look at records you can pay per record but this is expensive as you will open a lot of incorrect ones especially if you are looking for Reilly, however if you join for a period you can mess around at your ease, the marriage of 1866 also attached has only two children born after it, I have also attached those births for you to look at.
I had a look at migration records and this is a long shot and there does not appear to be children traveling would expect more. A Bridget Reilly travelled to NY age 21 in 1869 but from Hamburg, Germany.
Staying with this family and Miriams, Catherine I see a death of a Philip Reilly in the mid 1880s in Drogheda and a Kate Reilly present at death, again on this I see in the history of the St Peters RC church that a carpenter names Philip Reilly worked on it in 1881 at 5 Shillings a week. (About 35 US Cents in todays money).
I tried Ancestry for a Thomas Reilly mother Rice and got no matches but a lot of Thomas Reillys, tried the US and got some around the right year in the US but no mothers name, however he would not need naturalization if born in the US.
If we had a year of migration we could find if they all travelled together. If they went to New York they may be on Ellis Island site or there is a Castle Garden previous to that.
As an aside the the Reilly / Rice marriage found in Dundalk, Rice is a name there and I see one witness is a Finigan, your former Vice President Joe Biden (tree online free if you Google) is from the Cooley area about 5 or so miles from Dundalk. Also have been in touch with another man in NY who tells me a lot of people from this area settled in the Ovid area and are buried there.
You may be interested in a You Tube film of still photos called Ghosts of Drogheda, it is about 9 minutes and I find it enjoyable. The grave yard here in Drogheda in use at the time is Cord Road, it is closed to the public at the moment.
Is it possible to find out where your Reilly's died, that is Thomas's parents.
Regards
Pat