Design patents are not classified by the Cooperative Patent Classification system because the U.S. is the only country that issues what is actually called a design patent. One can use keyword and other field searching for design patents in the PatFT and AppFT databases. Then in the list of hits, those patents with a "D" in front of the patent number will be design patents. However, that will only find design or any patents issued since 1976.
A better way to search for U.S. design patents is to use the design classifications in the U.S. Patent Classification System. A tutorial is given below on how to do that. Many other countries offer similar protection to design patents called Industrial Designs. More information on Industrial Designs below.
Countries other than the U.S. do not offer design patents, but there is usually a registration system for industrial designs. Here’s background from WiPO:
“In most countries, an industrial design must be registered in order to be protected under industrial design law. Depending on the particular national law and the kind of design, an industrial design may also be protected as an unregistered design or as a work of art under copyright law. In some countries, industrial design and copyright protection can exist concurrently. In other countries, they are mutually exclusive: meaning that once the owner chooses one kind of protection, he can no longer invoke the other.
Under certain circumstances an industrial design may also be eligible for protection under unfair competition law, although the conditions of protection and the rights and remedies ensured can be significantly different.” http://www.wipo.int/designs/en/
International Industrial Designs are organized by the Locarno Classification system.