In principle you are trying to solve the DRM problem. As long as you cannot trust the runtime system, there is no complete solution. Your best bet is to store keys in system provided containers and hope those are well protected (i.e. the iOS key chain as borrrden already mentioned).
If that fails you can encrypt your RSA key with an AES key generated from some static information within the device. This should be thought of as obfuscation rather than encryption as the key is not really secret. You should probably try and use a standard container format such as PKCS#8 to encrypt the keys.
It is possible to generate RSA keys from a static set of data (using a PRNG to feed this data in the RSA key pair generator) but those kind of schemes are not standardized, very brittle and take an unspecified amount of CPU time, so I would strongly recommend not to take that route.