Either action caching or page caching would work fine; page caching would have the benefit of never calling the Rails stack, but it depends on whether you need to control who accesses that Json feed.
I'm a big fan of using page caching if you can get away with it - there are big savings on system resources to be had. :)
EDIT: Page caching example, in case there was any confusion:
class SomeController < ApplicationController
caches_page :index
def index
render :json => my_array.to_json
end
end
Unless I've misunderstood something, that should be all you need to do.