It is lovely to hear that you are looking for information on your ancestors and have traced a relative John Jenkinson back to County Carlow!
The John Grenham
website, a great place to search surnames and locations, has a few mentions of Jenkinson's a bit later in time, they may also be relations.
While having a look at the various websites, I also came across some details about a Jenkinson clan in Carlow and Galway with a John mentioned in 1749, maybe an earlier relation?
Hopefully, some of our members and industry partners can help as well.
What relation was he to you and did he leave the island of Ireland around the same time?