rockauto.com is quite inexpensive, but their supply is keyed to vehicles, so you'd have to know a vehicle whose struts are close to the size you want. Your setup looks like a single 12" (compressed / closed) length would be suitable.
Farm supply stores might have what you want, places like Tractor Supply or Northern Tool. Part of your problem will be finding struts that come with the mounting hardware, or finding a separate part / item for the mounts. The automotive struts are generally sold as replacements and do not include the mounts.
eta you might also consider what position you want the cover to sit in when open, horizontal for sun and rain protection? Or all they way up as you pictured. You can control / limit that with just the size of the air strut, or use something like a limiting cord (chain will rattle).
OR you could use something like the folding metal / locking bars used for chest and trunk lids, in woodworking.
Rockler has gas-spring struts, they're a bit expensive IMAO, $50 / pair
http://www.rockler.com/lift-o-matreg-gas-spring-lid-support