HI m1chael
Something to bear in mind when searching for the name Peter is that it has a common name variant of Patrick. There are a couple of Patrick May's showing in the 1861 census which could be Peter.
For example, in 1861 there is a Patrick May, b. 1858 in Liverpool, son of Patrick and Elizabeth living in Toxteth Park, Lancashire, (RG9; Piece: 2697; Folio: 23; Page: 49)
In 1871, not sure if the same Patrick (Peter?), there is a Patrick May, b. 1860 in Liverpool, living at a Boys Refuge in Liverpool, (RG10; Piece: 3792; Folio: 40; Page: 10)
Hopefully the marriage cert, as confirmed by Jen, will let you trace him back

Monica