That depends. Where was the child support order issued? (i.e. what court, in which state, in which county) Where is the principle place of business for Aramco? or from which State or country are the paychecks issued? If it's Riyadh and the support order was issued out of California the court here really has no power to issue a wage assignment order. Does he have property here in the U.S.?
I agree with Tobie. Aside from father putting his pride aside, he must be there to support your daughter. I speculate your daughter and you live in Los Angeles; therefore, since neither you nor the child reside in Oklahoma, you must register your child support Order here in California and pursue an action against father for child support. Was your case initiated in a Department of Child Support Services? Or otherwise did you open a case through a Family Law Courthouse? Depending on your answer, and although your options of enforcement are similar, collection process will vary.
You should consult with an attorney for futher guidance.
The good news is it doesn't matter where he lives, you can still get a child support order against him so long as you can get him served. Yes you can even have him served in Saudi Arabia. If his employer has a branch in the US you can serve a wage garnishment and have the support deducted directly from his pay. Moreover, the child support services will move aggressively against him if he does not comply with orders, which can limit his travels if he is using a US Passport.