Birds Underwater is the best by far, for a private tour you will have to specify your own boat and it will cost you though. If you go on a weekday the group boat might not be so crowded anyway and don't go near a holiday or on weekends as it is not just crowded for you all but too many people for manatee also.
http://www.birdsunderwater.com
Absolutely don't go with American Pro Dive. Trust me on this, I go up there many, many times each season. The changed owners a year or two ago and I don't want to go into how poor their standards are now.
An alternative to Bird's is a guy named Charlie Slider, I think he named his boat Aquamarine Images or something like that. He worked for Bird's for years so he would be my second choice as I went with him a few years ago when he worked for Bird's. But the folks at Bird's are still better.
GO EARLY, VERY VERY EARLY AM!!! 
Hope for a cold front. Manatee won't be there in force if it hasn't gotten a little cool. 
Allow as many days as possible. I've had viz of less than 3 feet at Three Sister's Spring (the premier spot) one day, and viz of 150 feet the very next day
Go figure. There are contributing factors but no one can ever figure it out. So many factors enter in.
Lots of stuff besides manatee, check out my website, diving cormorant, tarpon, freshwater turtles, gar at Rainbow River, etc etc. A fantastic experience and unrivaled photo subjects!!! 
Best, Carol