Slightly more up to date information then, cihb55, as of October 2009 the guide books are wrong. Both Syria and Jordan are quite happy to give (us Brits and Irish) visas and temporary carnets at the border. It might vary by border crossing, mind.
For a motorbike:
At Kilis into Syria: tourist visa EUR38 (UK) and EUR36 (Ire); carnet EUR60?; green card EUR22?
At Deraa into Jordan: tourist visa JD10; carnet JD20; green card JD7.50 (1JD==1EUR)