16-24VAC transformer with 40VA
A 220 VAC transformer can work without any problem on 240 VAC. The difference in voltage is not enough to cause problems. A 110 V AC transformer will burn because the difference in voltage is to high.

I suppose that your transformer from the USA indicates 110 VAC/24VAC 2A or something like that.In that case you need a transformer as mentioned 240 VAC/24VAC 2A. 

It might be that your transformer from the USA has to primary windings in parallel. In that case you could ask a technician to put both windings in series and you could use the transformer from the USA without any problem.

It is also possible to use a stepdown transformer as you indicated in your question.  240 VAC/110 VAC but with more than 50 VA because you have to compensate for the transformer losses.