Has anyone tried laying newspaper down between their plants to stop the dang squirrels from digging there? My garden is very small, only 3 x 6, so it would be practical in my instance. They have not so much nibbled at the plants as buried peanuts and other treasures, and in doing so cover up and undermine small plants. They also get into barrels and pots to do their thing. I may have to try KK's monkey cage trick.
Not sure anything short of a layer of screening or chicken wire will keep squirrels from doing what squirrels do. After a couple of waterings or rains the newspaper is soggy and falls apart, you might try cardboard and a layer of mulch instead.
There is a fine plastic netting, usually used to deter birds from eating orchard fruit, that may be of use to you. It is in the category of "screening" that Toni mentioned. You can lay it down directly on the soil, and the squirrels meet resistance when they dig. I think it should be available at big box stores, or even at nurseries.