Hi curlytops -
Welcome to Rootschat -
It may help you to look at the 1901 census for Mayo on the 'Leitrim Roscommon' site. There are some possibilities for your family there. I'm not sure if you know that both the 1901 and 1911 census for Ireland have been released but are not on line yet. All the previous census records have been destroyed. However the 'Leitrim Roscommon' has put a few counties on line.
Civil registration in Ireland began in 1864 (only Church of Ireland marriages go back to 1845)so for baptism and marriages before then you can usually contact the parish priest - if you know the parish.
There's a Thomas Frain(age 51) wife Bridget(49) andMichael,Tom,Martin and Mary Ellen living in the parish of Kilbeagh. The ages aren't always correct.
There are a few Dunleavys living in the parish of Kilmovee.
Here's the link -
http://www.leitrim-roscommon.com/index.shtmlSelect the 1901 census database -
Scroll to the bottom and click on the 1901 search page -
Select County Mayo
Input the surname in the'Head of Household' - you should get all the Frains
Try again but instead of 'Heads of H/H just put the surname in'Other Enumerators'
(this should give you the Frains living in other people's households)
You could do the same for Dunleavys.
Sometimes you can try to figure out relationships from the different households.
I don't know whether your relations are there but hopefully you may find something- if so you will know the parish.
Hope this helps
Regards
Neptune