Hi Bashford,
Maybe the marriage of Susanna & Edwin will help as it shows the witnesses. I would presume that Eunice C stands for Eunice Caffyn.
Slaugham, West Sussex, Date: 29 Jun 1837:
Susanna CAFFYN, botp (B)
Spouse: Edwin John BASHFORD
Extra Information: Witness wit: Hny. COOPER; Eunice C.
Found this marriage for Henry Cooper (not the boxer

) Perhaps Lois is Susanna's sister, making Henry her brother-in-law?
Slaugham, West Sussex, Date: 7 May 1836:
Lois CAFFYN
Henry COOPER, botp (B)
Extra Information: Witness wit: Hny. LEACH; Harriett LEACH
Hope this is of some help,
jane