They cannot be earned in any way unless you have been playing Animal Jam for a long time. Or if you are a member, with an Eagle, Owl or Falcon, you can play The Forgotten Desert to get the betas. Some betas are impossible to get from The Forgotten Desert. Some of the sought-after betas are:  Blue/Orange Mat Cami's frog Gecko Plushie Worn Blanket You will have people trading you rares constantly. Alternatively, look on people's trade lists for a beta and trade your best stuff for it. Go whichever way you prefer.

Summary:
Note that betas are items that were sold during Beta Testing. Know the betas. If you get your hands on a beta, put it on trade to get other rares.