Spring constant is approximately (all dimensions mm and for steel springs):

10^7 * wire diameter^4 / (outside dia-wire dia)^3 / number of coils

to give the newtons per meter spring constant. Change 10^7 to 10^4 to give newtons per mm

so 2mm wire with outside diameter 22mm and 20 active links (ignore ends) is

10 000 000 * 16 / 8000 / 20 = 1000 Newtons per m or 1 newton per mm. Too weak for an air rifle. Most air rifle springs are 5000 to 12000 Newtons per m spring constant.

Thicker wire, lower diameter and less coils = stiffer.