Most condo/house rentals are for one week minimums. Even hotel/motels usually have a two night min in the summer. Sometimes there is flexibility in June, but I would be hard pressed to accept a one night booking, as it hardly justifies the cleaning, prepping, post stay walk through.
The only way I can see it happening is through a private owner. Check listing sites such as homeaway.com, VRBO.com, shoresummerrentals.com and even Craig's list.
If you see some listings with openings, even it says one week min, send them an email and try to negotiate. On homeaway, you can change search critieria from number of bedrooms, number it sleeps or availability. You may have to "sell yourselves" (i.e quiet couple, non smoker, no pets, no parties). But maybe you'll get lucky!