Similar to artifacts, but they're drawn using an oekaki tool on the site, and then can be traded or bought with swap credits.
This could be a nice enchantment idea rather than a whole separate item system, that would make it a lot more doable. You'd have an artifact that has a card as an enchantment, and maybe we could add some filters to help identify what artifacts have cards.
That said I'm feeling a bit overwhelmed by the number of features and the amount of time going into the forum atm, the thought of trying to script in a whole drawing system is too much right now

I think if you/someone wants to develop the JavaScript side of this (e.g. a small drawing script that generates cards and exports them as an image file), then connecting it in on the server side would be way more doable for me.
My first impression is that id make them monochrome, e.g. you can pick an background and a pen color, but that's it. That would give them a unique look and might make the script easier.