So the draft notebook we have explains how to do fitting. The PR is here Bayesian copula estimation example notebook by drbenvincent · Pull Request #257 · pymc-devs/pymc-examples · GitHub Though that was started some time ago - it needs updating from PyMC3 to the latest.
I can try to make progress on this to get it over the line soon, but things are pretty busy at the moment. But maybe you can get something from copula-estimation.ipynb in the draft PR as it stands?