I currently have a 20"x2.125 tyre on my rim (think its and unbranded double wall rim).
Would a 1.9 tyre fit on? Looking for a non marking one and there seems to be a better choice.
Likely yes
Don’t see that being a problem.
Friend and I have the same 20" - Mine has a 20x1.75 and his has a 20x2.3
Both tyres fit fine. 
Thats a bit scary that both dont have the same tire.
Ok thanks. I thought it would be ok, just wanted to check. Tyre now ordered:D