Yes. All military personnel have a responsibility to support their children. Even without a court order, you can contact your military spouse's commanding officer to help arrange payments.
Use this military online locator service to find your spouse. The more info you enter, the better your chances of finding your spouse. You can also find your spouse by mail or by phone.
U.S. Army Enlisted Records & Evaluation Center
8899 East 56th St.
Fort Benjamin Harrison, IN 46249-5301
(Navy) World Wide Locator
Bureau of Naval Personnel
BUPERS-07 Customer Service Center
5720 Integrity Drive
Millington, TN 38055-3120
Headquarters US Marine Corps Personnel
Management Support Branch (Mmsb-17)
2008 Elliot Road
Quantico, VA 22134-5030
1-703-784-3941, 3942, or 3943
Air Force: HQ AFPC/DP1ORM
550 C Street, West, Suite 50
Joint Base San Antonio
Randolph, TX 78150-4752