If 1901 birthdate is correct then I think I've found her on last census born Beddingham, Sussex - think we are dealing with travellers with this one as abode was a tent.
The Patience who was a daughter of Joseph and Kate in Surrey (birth Dec.qtr.1904 Guildford) was actually born 23/10/1904 and baptised, as stated already. in 1905. This Patience went on to marry a Joseph Trigwell.
It doesn't look as Patience Chapman born 9/10/1901 had her birth registered as cannot find in birth index. As stated above, shown to have been born in Beddingham, Sussex.
The online tree is quite detailed regarding her children, and states her own parents as a Matty Coates and 'Polly' Chapman (believe she was Mary Ann Chapman). It appears that Mary Ann (Polly) wasn't married to Mr. Coates either as she was a Chapman. Having stated the names of her parents as Matty Coates and 'Polly' Chapman the owner of the tree has then linked Patience to the 1905 baptism in Surrey who was, as already stated, dau. of Joseph/Kate.
So, if the OP's Patience is indeed the one born 9/10/1901 then she was born in Sussex and from things looked at so far seems to be from a travelling family.
In that case, maybe this will need to be moved to the 'Travellers' board which might yield more results.
Annette