In reply to keffer:
Normally the charter traffic begins to kick in around Easter, but things seem to be late this year, perhaps because Easter's early. First week in May seems to be it. It will be a pain to get there before then.
Wikipedia is usually a pretty up to date place to find who flies to any given airport. Usual suspects easyJet, Thomson, Thomas Cook, Monarch, Ryanair, Jet 2. But nothing much in April, except easyJet from Gatwick or Glasgow.
https://en.wikipedia.org/wiki/Kos_Island_International_Airport
For info, Aegean Airlines flies MAN-ATH twice a week (Tues/ Fri) so you'd be able to get a through ticket to Kalymnos, but the times don't work well - either to Kalymnos or Kos. Fancy a city-break in Athens?
If you really do need to be there and back in the last week of April, and can find a way to get out there by going round the houses, it might work well for the return. Most airlines begin service on the w/b 30/4, so their inbound leg will be practically empty and dirt cheap. Eg £35 on easyJet to Glasgow or Gatwick. £70 on BA to Heathrow.
We did this (the other way round) for our first trip a few years ago. Out on the last easyJet flight of the season to Kos (which had approx 12 people on it, all of whom we saw again on the ferry!) and back on Aegean via Athens to Heathrow. Worked well.
Post edited at 21:55