Using Diffie-Hellman key agreement for generating a nonce should be safe as long as both key pairs are ephemeral, i.e. generated for each run of the key agreement protocol. Otherwise a man-in-the-middle can fool one of the parties in generating the same nonce over and over again.
Ephemeral Diffie-Hellman is however overkill for generating a nonce, as the nonce does not have to be secret. So what you can do is to generate a (random) nonce, and send it authenticated with the authentication tag to the other party, together with the initial encrypted message for instance.
To add the IV to the authentication tag, you may have to make it part of the additional authenticated data (AAD). GCM and CCM already include the counter and thus the nonce in the calculation of the tag. I'm presuming an authenticated block cipher with associated data (AEAD) such as GCM here.
Of course, if you have a good source of random numbers and enough bandwidth, you could just create a new (authenticated) nonce for each encrypted message.