I've used Airbnb in many places, but not CT...I have used arbaspaa.com for our two visits to CT...if you have no luck with airbnb (which I love, btw) you may give them a try - they run the gamut from rooms to B&B's and more (they also arrange group and maybe private tours of the area)...
Just make sure you read carefully the airbnb reviews and make sure the room or apt has the amenities you want (ac, wifi, laundry if you want it). If I see a few mentions of dirty floors or bathroom or noisy area or too hot/cold/damp or poor/no wifi, I'll pass it over.
We used airbnb in Rome and had an amazing apartment with a view of the Colosseum (it was steps away) for $150 a night...you can find some real gems!