While I don't know how the law works in other states, I can say that it is generally difficult to get any type of "restraining order" on someone out of state. The reason is because if he files for such an order outside of Missouri, the sheriff in that state won't cross the state line to serve it to you.
Theoretically, he could file for the order in Missouri if he doesn't live too far away from the county you live in. He would file for what is called an "order of protection." In order to get one, you need to show that you have experienced some type of traumatic event and are in danger of future harm. My guess is that sending a baby announcement in the mail isn't threatening at all, so you probably have nothing to worry about.
Here is a link to some information on our website about orders of protection and how they work.