I looked up the pin-outs for the two connectors then cut up a DB9 PC serial cable and used it to make an adapter.  It worked like a charm.

I found a couple DB9 PhoneNet adapter on eBay but they were a little pricey (compared to the DIN8) and I have a good sized collection of DIN8 PhoneNet adapters so I figured I would just use what I had if I could.