The states were beginning to keep B/M/D statistics in the late 19th century. Normally government actions begin in eastern states and spread westward. Check with the office of vital statistics (or similarly named agency) at the MO state captial, or the Stoddard County Court House.
Illinois may have adopted B/M/D registration earlier than MO. It has also been a leader in digitizing its records. An expert at searching these rcds is Charlene Reinhart. Look at her posts to genforum to find her e-address. See if she will help.