Apache issue with "Client does not support DH parameters > 1024 bits"

You are currently using a 4096bit DH parameter file, you would have to regenerate one for 1024bit or the developers will have to upgrade (sounds like they are using Java 6.0, if so try Java 7.0). Because this will reduce the level of security of your TLS configuration.

You can regenerate this file

openssl dhparam -out dhparam.pem 1024

1024-bit DH is not secure. It's likely that 1024-bit DH using common parameters is broken by billion-dollar sigint agencies; using custom parameters as dayotn967 suggested, they'll never bother with you, but they could. (Legal orders are cheaper than supercomputer time.)

You should tell your third-party "friends" to stop using garbage obsolete crypto in garbage obsolete Java versions.

Java 8 supports up to 2048-bit DH, which is large enough to be secure, though not as slow and hipster as 4096 bits.

Java 7 and newer also support ECDHE cipher suites, which are better in almost every way. (You should ensure they're enabled on your server.)