September's one of my favourite times of year in RMNP. I live an hour south and venture there a few times a year. Spanning the continental divide, you can expect different weather conditions depending on whether you are on the leeward or windward side of the park. Daytime highs are more likely to be in the 60s, but be prepared for overnight temps in the high 20s to low 30s overnight. At the very least bring some form of down or synthetic insulated jacket. A full-on parka is probably overkill, but I can't see where home is from your profile so I don't know what's 'normal' for you.
The other considerations are altitude and dehydration. Most of the park is over 8000ft, so if you're not acclimatized, plan to take it easy on distance and altitude gain in the first couple of days. Drink plenty of fluids - this is high desert. Given the low snowpack this year, by September many of the streams will have run dry. Check with the park rangers on water sources, but be prepared to carry more than in a normal year. Oh, and make sure you have a bear-proof food canister if you're camping below treeline.
Rain gear - always a good idea. Mostly mine is used as a wind barrier. You're unlikely to encounter many thunderstorms (peak season is much earlier in the year), but if a cold front runs through you may be dealing with some snow at altitude.