The most energy efficient way to cool these days is a mini-split a/c unit. In traditional ducted systems, a large amount of energy (up to 30%) is frequently lost through leaky ducts that run through inadequately insulated attic spaces and walls. With a mini-split there are zero leaky (or dusty or moldy) ducts, just an indoor air handler and an outside fan unit connected by copper line. While mini-splits are old news in much of the rest of the world, they are still relatively new in the U.S. What is most remarkable is that they keep getting more efficient every year. Efficiency is estimated by SEER (Seasonal Energy Efficiency Ratio) ratings. Ten years ago you’d be hard pressed to find a SEER 15 unit, ducted or not. Today the most efficient mini-split on the market is SEER 30.5 (Mitsubishi MUZFH09NA – MSZFH09NA).
The second most efficient mini-split currently on the U.S. market (I believe) is the a Fujitsu Halcyon 9000 Btu unit (model AOU9RLS2 + ASU9RLS2 indoor and outdoor unit), with a SEER of 27.2. This is what was recently installed on the 288 ft2 Studio Shed at the Micro Showcase so it can be used for year-round events. These units have the added benefit of heating as well, which new units can typically do down to 5 degrees F. The most efficient units are more expensive (installed cost was $3900, minus a $500 efficiency rebate), but environmentally it is hard to justify anything less.
Note that for small space applications, it it not possible to find a mini-split less than 9000 Btu, which may be oversized for some truly small well insulated spaces (under 200 ft2). In this case, 5-6000 Btu through-the-wall a/c units may be a better fit. Also note that for off-grid applications, mini-split units can have moderate phantom (standby) power loads that require a hard shutoff (at the breaker box) to turn off when not in use.
More information on conditioning small spaces on the Micro Showcase cooling and heating pages.