The picnic basket, which apprears at some random moment (*) on the central park or the beach, is a specific object that we don't have in our game files. (* From what I understand, they appear when some inactive Sims on those lots are hungry)
More accurately, we have them in our game files, since they pop up once in a while, but we can't access them. Even with testingcheatsenabled + buydebug, you won't find them anywhere in the build/buy menus. The one mentioned by Seabody is only for residential lot. Somenone corrects me if this has been changed with a recent patch.
The community lot picnic basket can be enabled through a 3rd party package that you put in the Mod folder. I've never used it myself, but it seems that this package just 'unlocks' this item so that the player can access it. (edited by moderator). If you are ready to use package files, just pm me and I will send you the links.