This printer appears to support printing on paper, panaoramic roll paper and cd’s. The panoramic prints will require the special roll paper and the cd’s generally require the printable type as well.
I see nothing about printing on other oddly shaped media, and the printer doesn’t look like you could fit a cofee cup into it.
I imagine, it will take some sort of tranfer paper to get this accomplished. Your manual will be able to guide you in the right direction if your printer is capable of doing this and it’s an advertised feature.