http://www.flyfishingyellowstonenationalpark.com/hatchch.html
Check out the above link for a hatch chart for Yellowstone Park...You will have to cut and paste it since I'm not sure how to make it a live link.
If I were going there with you this next fall I'd tell you to follow the chart and give yourself a "general" box to cover mayflies, caddis, and stones, that are listed there for that time of year, but concentrate on Baetis, Baetis, Baetis, and the standard ties for ants (including the flying variety), beetles, and hoppers...Don't forget Tricos especially if you are thinking about Hebgen Lake.
The Firehole may still be a bit too warm to fish well in September...Ask at a local shop...It is known as an early & late season "hot-spot". The Lamar/Slough Creek area may be more productive...If you are camping you can camp there and hike up to the 1st or 2nd meadow at Slough and the Cuts there will slurp down your hoppers, especially if there's a little wind about, which is the norm there anyway.
If you are anywhere near West Yellowstone and don't plan a visit to Blue Ribbon Flies, it would be like visiting Paris and not seeing the Eifel Tower...It is one of the premier fly shops anywhere and I'd say that even if Craig Matthews wasn't originally from Michigan! :)
Baetis...Do not miss this...It's very easy to do because you probably won't see them at first...If you see fish eating something/anything you are unable to see, tie on your Baetis imitation...You can thank me after!
Don't over do the fly thing...Tie for fun etc and so you will have something of your own to toss, but local knowledge is very important and you don't want to take the chance of missing something that may make your trip...Only Matt can actualy make it to "Paradise" every year :) the rest of us are left to day-dreaming of trips there. Don't mess up what may take you a long time to do again!
What I'm saying is stop in the shops and let them know you need some advice and buy some locally tied bugs! You are coming a long, long, way to visit a place that offers some of the best fishing in the world...A guide isn't a bad idea either...There are some shops that will offer up floats or guided trips etc...In 1995 I floated the Madison with a guide from the Madison River Fishing Co in Ennis and caught a 23.5" Brown that still puts a smile on my face 15 years later!
If you are really lucky Matt will chime in here but he plays his cards rather close to the chest :) especially when it comes to fishing out west...He may even tell you to skip over it and fish someplace else..."There's no real trout out west! Right Matt?! Maybe you should just fish the Driftless. :)"
Remember, "No lead weight allowed in Yellowstone Park!"
Spence