I shall have a look for you, I believe that Eliza may be a distant relative of mine somehow! Richard was Peter's father, correct?
Update: I've just found the marriages of two possible siblings in Keymer, father Richard Payne also.
Jane born 1829 m. 1853 Edward Upton
Sarah born 1826 m. 1850 Thomas Miles
There are also many other Payne marriages in the surrounding area, birth dates around the right time, with father Richard.
I haven't been able to locate a baptism or christening for Peter, do you have it saying his mother is Mary like you state in your original message?