Thanks to Google Books and Archive.org, We can go back to song collections from the 19th century and earlier. Rather than searching for the song title, I find it more effective to search for a distinctive phrase (or two) from a song, something that is not likely to change or have alternate spellings, and put that phrase in quotes.
There are lots of spellings of "Muirsheen Durkin," so I search for goodbye "sick and tired of".
I also search the Traditional Ballad Index and the Roud Index. In the Origins and DTStudy threads, we try to post every version of a song that we can find, and then we go to work analyzing what we've found.
I'm a big fan of the Traditional Ballad Index, so I try to buy all the significant books that are indexed there. Masato Sakurai and the Late and Legendary Q were able to amass even more books than I have, and we spent years posting everything we could find. I sure miss Masato and Q. And then there's Jim Dixon. He has secret, magical ways of finding things that nobody else can find. I suppose I could compile a list of at least 40 Mudcatters who have done amazing things here. It's kinda nice to think of them and the good times I've had collaborating with them.

-Joe-