Figs root so easily that most other plants can’t be rooted that way. Steve’s suggested method sounds like a good one. I’ve done something similar with some tough-to-root things (Luma apiculata, feijoa) and had pretty good success.
My only attempt to root goumi so far was trying something pretty different, more like my avocado rooting method, which only can form roots if the cutting has leaves on it (so not typical scionwood). I posted a photo when I took the cuttings in mid-May here:
I neglected them in their jar of water for longer than I meant to (almost a month) and then put them in a community pot of soil near the start of summer. I’ve removed any that died, but still have quite a few with green leaves, but no new growth yet, so I’m not sure about this method compared to what Steve recommends. I figure I’ll unpot them in spring to see if they’ve rooted yet by then.
I’m sure that @JohannsGarden could send you cuttings with leaves on them as well, if that’s what’s necessary to root them successfully rather than normal scionwood with leaves removed. Incidentally, those cuttings are from a bush that I got from him, and it is a seedling of Pippi.