Does the certificate say "Elizabeth Carswell M. S. McNamara" or "Elizabeth McNamara"? If the latter, it implies that Francis was illegitimate. In which case try looking for a birth of Francis McNamara in about 1894, mother Elizabeth McNamara.
Their son's marriage cert says Elizabeth McNmamara 'Ms McNamara' but can't find her wpuld have been born in 1871. Her parents were married in Glasgow.
There are a number of children in the IGI in the right time frame to a Thomas MCNAMARA and Helen/Ellen MCNAMARA.
The IGI lists 10 children to this couple (unless there were two couples of the same name having children at the same time - some of the births are very close together). The older ones were born in Scotland, and the younger in Ireland, and there is no sign of any of them in the 1881 census, so it may be that theye were in Ireland at that time, and that Elizabeth was born in Ireland.
The children include a Thomas, born 1870, and a John, born 1872, both in West Calder, Midlothian, suggesting that the family may have been there during the time of the 1871 census. Why not have a look at that? Also try the 1891 in case they had returned to Scotland by then. You presumably have approximate ages for Thomas and Helen from their 1861 marriage certificate?
I think 7 of the children match up, the ones in Ireland dont match.
[Have you tried Cresswell/Gresswell? I have found at least one whose name was variously spelled Carswell and Cresswell, and it isn't a huge leap from Cresswell to Gresswell.]
Tried all the variations I can think of. Peter Carswell doesn't exsist accept on his marriage cert.
I will keep trying
Susan