We went with Thomas Cook to cyprus when my first child was 5 months. They let me take a car seat, buggy as standard, then 20kg for my suitcase. Call them and ask or read q&a on their website.
We are going to cyprus in a few weeks, this time with British airways and they let you take a buggy and car seat for any child under 12 plus your suitcase allowance.
We will be taking the baby's car seat and luckily as we are locals, my family is arranging a car seat for my 4 year old so I don't have to bring two with me!!