I do not recommend mailing cash to the TX C.S. Disbursement Unit in San Antonio.
You can make cash payments to grocery stores. The store might charge a small fee for providing this service. You should receive a receipt and I highly recommend that you keep all proof of payments until your youngest child turns 22.
To find a location go to http://www.oag.state.tx.us/ to find a location near you.
You must fill out the retailer's payment form. It will probably ask for your full name, the custodial parent's full name, OAG number and the account number.