Hi Brian, sorry this is long but worth it, because it has the info to help
I have looked online for records for the Pelham family... interested in the Fox connection.
There are DEFINITELY records back to the 1700s for baptisms in Ireland, there are DEFINITELY multiple baptisms for PELHAMs too.. I know the surnames in Ireland were spoken and then recorded by the English, so the Gaelic pronunciation may not have translated into the English written form as we expect it too. I guess an example is Fox, when it is Fox, Fee, Foy, Fuchs... it depends who wrote it... so with Pelham, move the H and the name is Phelam... so please be flexible with looking... although I have been very strict in my search just to be sure, to be sure.
The Pelham family are related to the Singleton Copley family, from County Clare. The Singletons and the Copley's were both well known and 'GENTLEMENT' (they have a bit of $) and by the looks, there is a Singleton Copley that has relocated to London... which is probably where the Pelham family originated from. It DOES mention Henry Pelham is the nephew of the family. There is an image I have attached which is a Betham Genealogical Extract (info on how to get them in a moment...) This document is dated 1797 so right in the correct search time for you. It looks like the family are involved in the textile trade and shoe makers are seen a lot.
I have looked at multiple census on Family Search, for any Pelham born in Ireland up to 1830.... there seems to be a strong connection between the Pelham family and the shoe making trade, which does fit in with the areas of County Cork and County Clare..... but there are definite ties to Wexford. sorry if I repeat, I have a brain injury and forget what i said.
JUST a guess.... I think there are at least two Pelham brothers who were in Ireland in the 1790s... because I can see at least TWO Pelham MEN fathering children in Ireland 1790s-1810s... so Henry who was born c1784... and there is a John but I don't have an estimated birth year for him... but its possible Henry and John are brothers from London. Henry is the one listed in the Betham extract.
Just a GUESS.... Maria's parents may be the John and Maria... simply based on the mothers name...
there is a baptism of a Fran's (guessing Frances) born to a Joan's (Joannes/John) and Marae (Maria/Mary) on 5 August 1797 but the baptism is at St Andrews in Dublin (not unusual for baptisms to be in Dublin even if the family were somewhere like Cork or Clare in my personal experience with family research).
there is also a William Pelham born/baptised 1798... so this could be a sibling or cousin for your Maria too. No parents mentioned. Also says baptism Dublin, but no more detail yet (guess it would be the same parish).... he ends up having a son James Pelham in Ireland in 1825 with wife Julia Brown. He appears on the census in England in 1851 in Manchester.... as a shoemaker. His family search ID is M35W-DGC
There is definitely a William and Mary plus a John? and Maria/Mary in Ireland and I guess either couple could be your Maria's parents.... so it may need digging from you, but I feel that is more than we had before we looked today. There is also a Henry... not sure exactly where he is but he has been in Ireland.
There are a lot of possible cousins for Maria, could be siblings, that have moved to the US.... and there are a few that have Henry repeated, so likely Henry's descendants.
For a more specific location, I can see a Hannah Pelham is mentioned in a baptism in Youghal Cork in 1817 for a Sarah Pelham.
There ARE Tax Assessment records for Pelham's in Wexford 1830s.. attached...
OOH... YOU HAVE A LORD IN THE FAMILY.... LORD Pelham...
LORD THOMAS PELHAM is mentioned in DUBLIN in 1712.... so way before 1794! He is mentioned in the COURT of CHANCERY books, that's another one I will leave you to explore, but I am happy to help if you need. Not sure where in the world you are, but I am used to digging up my Irish ancestors... and helping others.
Then in 1803 there is STILL a Lord Pelham mentioned... in Ireland... Court of Chancery again in April 1803.
Going to start another comment, so I can keep up with myself :D
but to search for the Betham extracts I mentioned....log onto FAMILY SEARCH, its free. type in T search just for the surname Pelham, with the location being Ireland, the dates 1700-1840. Then look under COLLECTIONS, look for the group of OTHER collections, then look for IRELAND BETHAM GENEALOGICAL EXTRACTS.... because in there, I found some information for you.
Hope that helps, I am excited and OFF to find some Pelhams in Ireland.... hoping they are in some books because they are gentlemen
Cheers