Can I use two 30amp breakers instead of one 60amp?
You definitely do not want to do this. One of the reasons is if one of those 30A breakers were to trip it would leave the other half of the circuit to carry more current than it would normally be safe for it to handle. 

Sure you might say that if the second breaker circuit saw a current overload then that breaker would also trip but this is not always assured. A 30A breaker is not going to instantly trip at say 30.001A. Whatever operating margin that second breaker would allow continued current to flow to the load overrating the 30A conductor on that half of the circuit.

So do this right and install a 60A breaker and new wiring suitable for 60A circuit.