Just wanted to show my results.
I liked the idea with the plain coin boxes, but before I found a price-reduced Toniebox I got a 3D printer (BambuLab A1 mini). So my base case was this model:
NFC Case with magnet - Tonie Base - Parameterized by c-l-a-v-o - MakerWorld
Despite the case has a diameter of 4cm and the NFC-Tags I received from RFIDfriend are smaller, I went with it. The size suits the Toniebox better and the images are larger.
Adding some hot glue for extra weight.
Printing the images on photo paper so they have nice colors.
The material costs are about 1,50€.
Together with a bunch of these custom Tonies I gave my kids two original Tonies borrowed from a friend. I feared they would ignore the custom ones, but in fact they did not use the original Tonies. 
The cases seemed to be more interesting
