Tomolloy,
A good resource to check for baptism registers for Tulla is the Clare Library...clarelibrary.ie. There you can search the genealogy section, select the parish, and view the registers using a date, or either parent's surname. There are no surnames with a Maroney or Marooney spelling, but there are five John Moronys born between the years you mention. If you know his siblings, if he had any, those are there too so you can figure out which one is your John Morony. There are a few more that are a couple of years earlier or later than the dates you mention, so you should not exclude those in your search.
I just reread the last past of your question regarding speculation on his parents'names...in the registry, there are entries for those names. See entries # 4092 - 4094 as well as # 4145. You will see mother's names as Hardgrove/Hargrove. The names "Ane: and "Nance" are synonymous. It could be that Ane was mistranscribed leaving off the letter J. You will see the residence of "Lah (?) in three of the entries, and Teeragh in the fourth one. Other entries on the register show Teereda and Lahardan...those might be the correct place names, but I could not locate them on townlands.ie.
In any case, my best guess is that these four children - Mary, 1839; John, 1837, Patrick, 1841; and Bid, 1846 are all children of James Morony & Ane/Nance/Jane?? Hardgrove/Hargrove.
Regards,
