Nice puzzle! But unfortunately it can not be transported so easily with the pennies (€-Cents). The pennies fall around, or you do them in an extra container. Somewhat uncomfortable, constantly the worry about the pennies!
 

A suitable case, that would be a solution!

Designing a suitable case has its problems, of course. It should fit tightly, so that the tablet can not slip out. 

The outside cent piece does not need a cover, as it fits very tightly. It also serves as a tab to pull out the tray.

The cover must be printed upright. So ensure a good grip on the printing plate!

Remark: As all parts are designed to fit very precisely, it may happen that you have to rework one or the other part a bit with sandpaper and/or cutter due to different dimensional accuracy of the printers and the different behavior of the filaments.
 

Dimensions:

Width tray (printed): 62.7 mm
Interior width case (designer): 63,5 mm

Height tray (printed): 4.1mm
Interior height case (designer): 4.5 mm

As different trays exist, I have attached the "Coin Tray" file from KamikazeGrandma here.