Hi Mike,
I think that I may have an answer for you...emphasis on think! First of all, the parish baptism records for the RC parish of Murragh/Templemartin go from 1834 to 1864, and that is why there is no parish record for the twins. I do think they are a part of this family though. I also found another sibling, but first to explain Patrick's record. It shows his mother as Ellen Allen, and I think that is an error in writing down the name after hearing it OR possibly a derivative for Hallihane, Hallahan, etc...If you Google the surnames Allen and Hallahan, they share sort of a common Gaelic root of "aille" and "aluinn"...both referring to beauty or being handsome. In any case, I think it was heard incorrectly. Attached is their marriage record, and one of the witnesses was Thomas Allen of all things. On Patrick's baptism record, Ellen Leary is one sponsor - probably a relative of Denis.
I am unclear now regarding your initial post with the names Barry and Holland....do they have anything to do with this? Or were you just giving random names as an example?
Johanna Leary, 9 Mar 1861 is another child of Denis Leary and Ellen Hallihan, residence - Scrahn, Murragh & Templemartin, sponsors - Daniel Leary & Catherine Halihane.
I must say that 12 years is quite a span between the birth of Johanna and the twins, but I could not locate other children....not totally unheard of though.
In case you're interested, I did see parish baptism records on irishgenealogy.ie under the church records tab for Ellen Hallahane (26 Jul 1835) and Denis Leary (22 Dec 1835)...they could be your couple.
Your very first attachment above doesn't relate here because it is from the RC parish of Bandon in March 1834.
Finally, there is an excellent article on IRO that you can search for entitled Irish Naming Conventions and Baptism Traditions that provides a lot of good information.
Regards,