I've never come across anyone looking to teach in Syria before!
The following is taken from 'Teaching English Abroad' by Susan Griffith:
The opportunities in Syria are expanding and improving. The Education Adviser at the small British Council office in Damascus is willing to advise individual enquirers and has a list of half a dozen ELT institutions in Syria. The British Council cautions that: 'Teachers wishing to teach here should make sure of their positions before arrival. They should obtain sponsorship from the prospective employer for residence purposes and have an agreed written contract.'
Contact details for the aforementioned British Council office can be found on the following link: http://www.britishcouncil.org/syria-syr ... act-us.htm
Sorry I can't be of more help!