Yet another day that I am thankful that I can walk into my local building department and pull an owner/builder permit to replace an entire panel, upgrade a service entrance, convert from overhead to underground feeder, add a sub-panel (combiner panel), and add an entire 4400W PV array to the roof without the need of a "licensed electrician". The diagrams I drew for the main panel upgrade permit years ago were hand-drawn on notebook paper. The three line diagrams I drew myself (in autocad) for the PV array already passed the state of FL PE review for NEC 2011 compliance ($250 review fee, not a permit).
Minimum permit fee is $50 where I live, so I like to get my money's worth and pool the simple little projects like the one proposed by the OP.
Don't expect to be able to re-use two 30A double pole breakers to feed one 60A sub-panel. Whether you can actually feed a 60A sub-panel from your existing panel is the first question to answer. That is why other responses include requests for photos, and requests for manufacturer and model number of your existing panel.