You might be in luck here! In the US, patents last for only 20 years. Since, the Game Boy was released in 1989, any patents are long since expired.

Using the Nintendo logo might (NB: Not a Lawyer!) be permissible if it's required for software to run on the hardware. This was a big part of the Sega v. Accolade case.[1]

There are still new games being released on cartridge for the original Game Boy. The most recent I'm aware of is Ruby & Rusty last year.[2]

[1] https://en.wikipedia.org/wiki/Sega_v._Accolade

[2] https://www.bitmapsoft.co.uk/product/ruby-rusty-save-the-cro...