They can only say no, right?
It would be amiss of them if they did......surely they must know that 
It isn't as simple as all that. Almost every parish is down to only having one priest. Try finding a parish where the priest is actually at home and has enough time to stand over someone while they search through records, they couldn't allow a stranger time alone with valuable historical documents as it isn't the first time a page or two has been torn out and taken.
So, try making an appointment, don't just turn up and expect to be let in!
The priest at St Patrick's is Canon Hill, I think he's on his own there. At Carfin it's Father McGachey, he's a very busy man as he has Carfin Grotto to administer. There is a Decon there but I don't think he lives in the presbytery and may only be at the church on weekends.
so, better to make an appointment. (and be nice, lay it on thick, plenty of honey and you'll catch more flies!)