This is not a definitive answer to your question, just my observations. If your John Carter married in 1677, my best guess he was born about 1655. (22 has been the common age of marriage for males in my experience in this area of the country). This means that John was born at the height of the Civil War which presents three challenges.
1. People moved around a lot as the war progressed.
2. The keeping of parish records was changed for a time and are probably incomplete.
3. There was a significant rise in nonconformity during this period, particularly in the Bedfordshire / Northamptonshire borders. Many new groups started and not all their records survive (some do).
Having said that, there are two christenings that might be of interest to you. There is a John Carter, 29 Jul 1655 at Potton, Bedfordshire: Father: Andrew Carter but this is not the only one in Potton around this time (several other John Carters between 1650 and 1657 in Poton). There are others in Bletsoe and Clophill. John Carter, 30 Jan 1654/55, Bletsoe: Father: Joseph Carter. Bletsoe is only 8 miles from Irchester.
I think you will need to reconstruct the Carter families in the area, but you have a few too many Johns to choose from!
