Christopher Carter and Ann Sanderson were married in Westerdale in 1742 and had three children that I know of in 1743, 1751 and 1761. This information was from the IGI.
A transcript of the baptism record of one of their grandchildren from 1780 states that Christopher and Ann Carter are of Danby.
The IGI also has the following information for Christopher Carter Birth: About 1717 Of Danby, , Yorkshire, England and his wife Birth: About 1721 Of Danby, , Yorkshire, England
I am not sure about the source or reliability of those two approximate birth dates and have been trying to find any birth/baptism records for either of these two individuals.
I've looked at the transcribed Danby parish records for christenings between 1711 and 1734 on An***try and there are no Carters at all, several Sandersons but all boys, no Anne.