Since I will be changing the wheel size on the Birdy from the stock 18" 355 to the new 20" 406, I will also need new tires and inner tubes. For 20 inch 406 tires, there are lots of choices as it is a very common tire size.
The limiting factor here is the frame clearance during folding, and the rear derailleur cage clearance during riding. I understand from others' experience that for this larger 20" 406 wheel size, I cannot use a tire that is too wide, as it also makes the tire outer diameter too big for proper folding.
My preferred tire for 20" 406 is the Schwalbe Kojak 35-406 tire that is 35 mm wide, as it provides the best balance between comfort and rolling resistance. However, it seems that this tire width may be too wide to be used on the Birdy. The next best option is thus the Panaracer Minits Lite tire, which comes in a slightly narrower 32-406 tire size.
I have used this tire previously in the narrower 28-451 size, on the Dahon MuSP and also the Fnhon DB12. The 32-406 size was briefly used on the Dahon MuEX many years ago, but it was replaced as it did not feel suitable at that time.
Panaracer Minits Lite folding tires.