So, puzzle games are quite a different animal, musically speaking than most other genres. It's hard to find a 'general' rule of thumb when writing music for them, which is probably why the soundtracks for puzzle games are so eclectic (just compare the
to
for example). This could lead to some difficulties in finding stock music that satisfies the qualities you're looking for.
It is very possible to write slow, yet happy-relaxed music that satisfies a turn-based game, and you may want to seriously consider hiring someone to do it for you. Based on the art that you've presented, it looks like to me like you may be looking for music that is slightly darker but still cute, and doesn't produce too much of a sense of pressure for the player, as the turns are not time based. In this case, you may want something more 'ambient' sounding and less structured. Try searching through the
BandCamp tags, like ambient or downtempo. Based on the art, it also looks like you may want something 8bit or 'chiptune' sounding, which you could also search for on BandCamp.
I realize a lot of the words I just used are also listed in my signature as a description of me, and I only hope that it's a coincidence and not my sub-conscious shouting at me, but all the same; I think it is a musical direction you may want to consider. I've written some
8bit style music I would be willing to let you use if it fits for your project, but I think you'll want something more customized. Let us know if you find any stock music that fits; I'm pretty curious just intellectually to see what will work.