Hi
The GRO is the general records office where you can obtain birth,marriage and death certificates from. If you have a rough idea of the year for a small fee you can search online for the details which would enable you to apply for the certificate.
You can search for the details at
www.1837online.com once you have found the correct birth for James you can apply from that site for the certificate which would give his mother and father.
Another site to try for the bmd details and this is free to search
http://freebmd.rootsweb.com/always worth looking at that site first,records are being added about once a month or so,so keep checking back.
Here are the family in the 1891 census
address North Road
John Stanley, head, married, age 47, tailor, born Cumberland Keswick
Ann Stanley, wife, married, age 45, born Cumberland Keswick
Mary Ellen Morton, daughter, married, age 23,woollen feeder born Cumberland Millbeck
Susannah Stanley, daughter, single,age 20,woollen feeder born Cumberland Applethwaite
John Stanley Jr,son, single, age 19,woollen spinner, born Cumberland Applethwaite
George Stanley, son, age 17,woollen warper, born Westmoreland Newbiggin
Miles Stanley, son, age 15, warper woollen born Westmoreland Newbiggin
William Stanley, son, age 12 born Westmoreland Newbiggin
Robert Stanley, son, age 10 born Westmoreland Newbiggin
Margaret Stanley, daughter, age 8 born Westmoreland Newbiggin
Charles Stanley, son, age 6 born Westmoreland Newbiggin
Eva Stanley, grandaughter, age 3 born Yorkshire Ravensthorpe
Annie Stanley, grandaughter, age 1 born Yorkshire Ravensthorpe
Fred Morton, son in law, married, age 25, scribbler cleaner, born Yorkshire Hopton

I have a feeling the grandchildren may well be Morton not Stanley although on the original image they are listed as Stanley.
Civil parish: Mirfield
Ecclesiastical parish: St Saviour
County: Yorkshire
Source information: RG12/3730
Registration district: Dewsbury
Sub registration district: Mirfield
ED, institution, or vessel: 19
Folio: 77
Page: 30
If you would like any other advice please post and there are a lot of very kind people on this site that are only too willing to help.
Nicky