The list of Signature Algorithms (constants) is very limited! Fortunately the newer versions of php/openssl allow you to specify the signature algorithm as a string.
You can use the 'openssl_get_md_methods' method to get a list of digest methods. Only some of them may be used to sign with RSA private keys.
Those that can be used to sign with RSA private keys are: md4, md5, ripemd160, sha, sha1, sha224, sha256, sha384, sha512
Here's the modified Example #1 with SHA-512 hash:
$fp = fopen("/src/openssl-0.9.6/demos/sign/key.pem", "r");
$priv_key = fread($fp, 8192);
$pkeyid = openssl_get_privatekey($priv_key);
openssl_sign($data, $signature, $pkeyid, "sha512");