Are any of Israel's neighbouring countries bound by the Hague Convention?

No. None of the Israel's neighbouring Arab states are signatories to the Hague Convention on the Civil Aspects of International Child Abduction. The concept of parental authority and rights under Islamic law is very different from the guiding principles behind the Convention.The only Arab state bound by the Hague Convention is Morocco, though it is not a close neighbour. It became a Hague Country in 2010. The Hague Convention is in force regarding child abduction between Israel and Morocco, as of 1.6.2010.

Hague Convention