I went out to YNP in 2003 right around the 4th of July, and people were telling me then that I was just a bit early for the 'good' fishing. I still had a great time. I've been to the shop for GYFF as recommened above and they run a great shop and can certainly give you what you're looking for, although its going to cost!! I also highly recommend you take a look at Randell Ziegler as a guide
His prices are low compared to other guides in the area that I checked on (not sure if he does pack-in trips tho), and his float down the yellowstone river is AMAZING. Randell also said I should try the Lamar river in the park but when I checked with a fly shop in Gardiner they told me the Lamar wasn't fishing well due to all of the runoff at that time of year. Slough Creek was fishable but was CROWDED - although at the time you're going it might not be too busy. I mostly stuck to the Madison River inside the park and had it mostly to myself and caught 'enough' fish.
If you've never been to YNP, plan on at least 1 day of NOT fishing just to get around and see everything. Have a great trip, its one you won't forget!