It's sometimes possible to work out a maiden surname by checking for possible marriage matches, but there are so many James Nolan marriages in the area that I dont think that's going to work in this case... I'm also not certain that the 'years married' entered on the 1911 census is accurate - the form has married 12 years so c1899, yet on the 1901 census they have a son Peter age 13, so born c1888...
Probably the best way to try to trace the maiden name, and then the marriage would be to try for a birth cert for one of the children. The most accurate age seems to be the one for Catherine - i.e. about 7 months on census day, which was 31st March 1901. If this is accurate it would mean she was born somewhere around the end of August or beginning of September.
There are two good matches for Catherine/Kathleen's birth on the BMD Index on FamilySearch, and unfortunately one of them seems to be missing the reference numbers needed to order a research cert from the GRO :
Name: Catherine Nolan
Registration district: Carlow
Event type: Birth
Quarter and year: Jul-Sep 1900
Volume : ? / Page: ?
Name: Kathleen Nolan
Registration district: Carlow
Event type: Birth
Quarter and year: Jul-Sep 1900
Volume: 3 / Page: 295
There are two other Catherine Nolans listed in Carlow registration district during 1900, but both are in the Oct/Dec quarter - so presumably too late for your Catherine.
I think that the 1st one may be the better bet, since that's how her father spelt her name on the census returns. You could try contacting the GRO to see if they will do a search of the Catherine/Kathleen Nolan births during 1900, in Carlow district for you with father's name James. The phone numbers are at the bottom of this page
GRO Roscommon, ContactSee :
Ordering Certs from GRO Roscommon Details included on a Birth CertShane