Organizations? None that I know of, at least not a well known respected organization. However, some of the well known training centers such as Rangemasters, Suarez, etc. have their own instructor certifications. Some of them are fairly rigorous as they don't allow just anyone to attend and get their certifications without really knowing their stuff.
Of course, as already mentioned some of the various states have their own certifications for conducting CCW/CHL licensing courses. The Texas Department of Public Safety (read highway patrol/LEO) conducts the week long handgun instructor certification course for CHL instructors in Texas. They have an abbreviated course for those that can show proof of previous handgun instructor certification through LEO, Military or NRA. The premise is that these already know how to teach and just need the core legal knowledge instruction to be able to teach students the laws concerning deadly conduct, etc.