I have seen several posts with regard to the above. Unless a US person is coming to Cyprus with a contract of employment already in hand I believe it is quite difficult to iobtain immigration papers.
Whether this is to do with the fact that Cyprus are joining EU in May and will no doubt have to allow citizens of EU states reside here so may wish to stop a majopr influx of persons, I do not know. I will try to find out more and report back.
Vivian