The best time to visit Cyprus with a baby or toddler is during spring, when the air is warm and balmy and there are wildflowers everywhere. If possible, visit during Greek Easter when there are loads of events going on in towns and villages across the island.
During the summer, hotels, restaurants and all the attractions will be open, and there should be numerous activities and festivals to keep you occupied. However there may be overcrowding and inflated prices. The heat in late July and August can be stifling and should be avoided. If you are visiting in then, make sure you’re in an air-conditioned hotel and are driving an air-conditioned car.
The autumn, too, can be hot and humid, so don’t bank on cool, pleasant weather in September or even October. During winter your experience of Cypriot life is likely to be far more authentic and less touristy, but a lot of places will be shut, and the weather will be more unsettled and even quite cold.