There's a large cluster of Cavanaughs/Cavanaghs/Kavanaghs/Cavenaghs in Kilglass Parish, County Sligo. I've been through all Kilglass and Easkey parish's baptisms and marriages on microfilm #1279204 from LDS, although there are still some other parishes. I've written down every single Cavanagh, with every spelling variation and put them all into family groups. This is how I eventually found my Cavanaughs (which took years and finally was found when I got my GG grandfather's sister's death record with her parent's names on it, and her parents were in my database of Cavanaughs.)
I do not have a single Timothy Cavanagh in my database, so it's unlikely (but not impossible) that they were in Kilglass Parish, County Sligo.
A few thoughts....
Do you know where Timothy married? US or Ireland? Where were his kids born? The Catholic Church in Scranton will do marriage and baptism look ups for a fee. My earliest records from them were 1868, but they may go back further.
You might try looking up the Scranton Directories (pre-phone book) and you might get a residence and if his wife outlived him, she might remain in the directory in subsequent years, listed as "widow to Timothy." This may help you isolate when Timothy died.
The state of PA kept death records from 1906 on. If you have a date of death, they can get you the certificate, which typically would have parents listed on it. If he died before 1906, you can go to Albright Library in Scranton and go through the microfilms (if you can narrow it down to a few years, it will save you a ton of work.... ask for the index film and be prepared to give a driver's license to get it). The information on them is very little, but it could possibly provide a lead.
Griffith's Valuation has this Timothy Kavanagh in County Mayo (spellings varied based on who wrote it, not how the family spelled it): http://search.ancestry.com/cgi-bin/sse.dll?indiv=1&db=gr...
If you can isolate when Timothy's wife died, you might generate some leads there. If they died in Scranton, they're probably buried in Cathedral Cemetery (formerly Hyde Park Catholic Cemetery), but the records before 1920 or so are pretty poor. Still, I've had some lucky finds.
If you know of any of Timothy's siblings, and if they died after 1906, you may be able to get a death record with parent names.
Hope that helps!