First thing you should do is try to raid whoever got relegated for their better playes, since not many would want to play in such a league. Then proceed to the free transfer pool. Plenty of players are released every season and those who are past their best are willing to go to crappy leagues where they can still do a job.
It's gonna be very hard for you to attract big names right now, but if you are succesful domestically and manage to become a regular european fixture you may attract some decent names in the future and you'll probably increase your league's reputation. In one of my longer saves, playing in Austria, 5 seasons in some pretty good players are already willing to join my club (Adebayor, Aquilani, among others).
Also, if you can get your hands on some good scouts, send them over to Africa as you can get good players for chips regens in Africa spawn on the 13th (or 15th, I'm not sure) of January and you can often find a few jewels there, which not only become good players but also have resale value. I'm not aware of league rules in Ireland, but if there are WP restriction or non-EU caps send scouts primarily to the Maghreb (Morocco/Tunisia/Algiers) as many regens over there have dual nationality (French) which will prove helpful.
Best of lucks!