A simple program which will detect the maximum Diffie-Hellman size supported by the JRE.

Diffie.java

import java.security.AlgorithmParameterGenerator;
import java.security.InvalidParameterException;

public class Diffie {
    public static void main (String[] args) throws Exception {
        AlgorithmParameterGenerator apg = AlgorithmParameterGenerator . getInstance ("DiffieHellman");
        int good = 0;
        for (int i = 512  ;  i <= 16384  ;  i += 64) {
            try {
                apg . init (i);
            } catch (InvalidParameterException e) {
                break;
            }
            good = i;
        }
        System . out . println ("maximum DH size is " + good);
    }
}

I think if you count the loop downwards it is faster to detect the first success (at least if you then actually call #generateParameters()). The used size in JSSE for TLS is btw capped by the provider max, but could be less: https://docs.oracle.com/javase/8/docs/technotes/guides/security/jsse/JSSERefGuide.html#customizing_dh_keys

Thanks for your quick test. I just wanted to state that this script does not work for a check for 2048bit, because java 8 allows these 64bit steps only up to 1024 and then 2048 with no steps in between.