Hi again, I may have found the baptism notice for Brigidam Mulligan August 1817 parents being Jacobi Mulligan and Margeritae Manion. St Peters and Drum . Not sure how to verify this however. Maybe see if I can find Michael and John Mulligan?
I fear you may be falling into an all too common potential error, one usually denoted as "looking under the lamp posts". That is, looking in locations where records exist, while the records for the correct location simply don't exist.
It is highly likely that your Brigid Mulligan and Malachy Fallon were born before the start of the relevant registers. The Killenvoy/Knockcroghery registers only start in 1841. If that is where they were from (as it appears), then you simply aren't going to find their baptisms, or marriage either. They were farmers, and farms don't move much (farmers can, but rarely).
Fallon seems to have been a common enough name in the area, and Mulligan is a well known Irish name. Given a number of early enough registers in that area, you will find baptisms with those names. But are they likely to be yours? If further away than an adjoining parish than probably not. In any case, without addresses it becomes difficult to be sure, even if you find one in the same parish - as you have already discovered!
As an aside - it is possible that the Killenvoy registers only start in 1841 because a previous larger parish was divided, such that earlier records might be in an adjoining parish. I have that sort of knowledge for the Diocese of Ferns, but no idea for Elphin.
