I found a useful tool for inflating the tyres of A-bike and other tiny wheeled bicycles on the website of Topeak recently:
http://www.topeak.com/products/Mini-Pumps/Pressure-Rite
With this tool, you can use a normal bicycle pump to inflate the tyres of your A-bike now!
Of course, you have to use a pump which is capable of inflating the tyres up to 90psi and a model with pressure gauge is recommended.