Hi Rohan,
When you don't find the IP Phone model listed in the Device defaults you can either install the required Device Pack (which adds the Firmware as well) or upgrade to a supported later CCM Version. Here is the minimum required device Pack for the 7937 and CUCM 5.1(3);
Cisco Unified CallManager Device Package 5.1.3 (6104-1)
Release Notes
http://www.cisco.com/web/software/282074299/26749/cmterm-devicepack-5_1_3_6104-1_readme.html#_Toc206327231
From this path;
Support> Tools & Resources> Voice and Unified Communications > Cisco Unified Communications Manager Version 5.1 > Unified Communications Manager/CallManager Device Packages > 5.1(3.6104)
Hope this helps!
Rob