I think that your William was christened with the surname Cullabine at Barlborough, slightly north west of Mansfield. According to some records of dad's there were quite a lot (20) with this surname in the area from about 1750 onwards, so they probably tie up with our branch of the family at some stage, who were from Mansfield.
The card appears to be from the Mormons, it is numbered Page 6,411.
I can't work out the name of the parents from the card, but hopefully with this information you will be able to find out those details.