I know anything centerfire is legal in MO as I hunt there too, but no .22 bullet is adequate for deer.  A .243 is not really enough caliber either.  If you shoot enough deer you will lose one sooner or later, even with a well-placed shot.  If you MUST shoot a deer with this gun use the new Nosler Partitions, as they are the only thing out there with any significant chance of a clean kill. They are 60 grains and only available to use if you handload.  Keep in mind the problem with small calibers is the size of the leak hole.  You will have no blood trail whatsoever.  The neck is an iffy shot at best, especially with iron sights.  The spine is only 2" thick and moving unpredictably.  Better to relegate your poodle shooter to its rightful place and get a deer gun in .30 caliber.  It just is not ethical to shoot a deer and know in advance there is a good chance of not recovering it.