Most private keys are essentially just random numbers, so if all you want is a private key, you just need to use a high-entropy random function to generate your private key that's 256 bits.
Converting those bits into something a normal bitcoin wallet can understand (like WIF) is a little trickier, but the process is spelled out here. I'm recapping the actual process here so you can use the Java library java.security.MessageDigest for SHA256 and you can use this code snippet to convert to Base58.
1 - Take a private key
0C28FCA386C7A227600B2FE50B7CAE11EC86D3BF1FBE471BE89827E19D72AA1D
2 - Add a 0x80 byte in front of it for mainnet addresses or 0xef for testnet addresses. Also add a 0x01 byte at the end if the private key will correspond to a compressed public key
800C28FCA386C7A227600B2FE50B7CAE11EC86D3BF1FBE471BE89827E19D72AA1D
3 - Perform SHA-256 hash on the extended key
8147786C4D15106333BF278D71DADAF1079EF2D2440A4DDE37D747DED5403592
4 - Perform SHA-256 hash on result of SHA-256 hash
507A5B8DFED0FC6FE8801743720CEDEC06AA5C6FCA72B07C49964492FB98A714
5 - Take the first 4 bytes of the second SHA-256 hash, this is the checksum
507A5B8D
6 - Add the 4 checksum bytes from point 5 at the end of the extended key from point 2
800C28FCA386C7A227600B2FE50B7CAE11EC86D3BF1FBE471BE89827E19D72AA1D507A5B8D
7 - Convert the result from a byte string into a base58 string using Base58Check encoding. This is the Wallet Import Format
5HueCGU8rMjxEXxiPuD5BDku4MkFqeZyd4dZ1jvhTVqvbTLvyTJ