You'll have to get the approval from the judge. I suppose you can file a joint motion asking for the adjustment and explaining how you came up with the revised amount and that your ex is willingly going along with it.
Here are forms and instructions from the Missouri court system.
Why would the recieving parent file for and obtain child support and then immediately want it changed? Something doesn’t sound right. Expect a court to be suspicious of the desire to change the obligation.
Is the other parent receiving state benefits (welfare) for the child? If so, then it is likely that the state wants to be reimbursed for the expenses, and cancelling the child support is not an option.