Answer: There are no proven gopher repellant plants, nor is there a list of plants gophers avoid. They aren't really attacking your plants on purpose, they just happen to destroy the root systems while digging their tunnels in search of insects. There's really no way to completely control gophers, but you can try trapping them. Some gardeners have had good success in repelling gophers by stuffing bars of soap down the holes, or wads of human hair.
As for the planting area you describe, it is not only shady but it's probably dry, as well, because of the tree roots. Tree roots will compete with the roots of other plants for moisture and nutrients, so choosing plants which grow well in dry shade should ensure success in the flower bed.
Here are a few suggestions for plants that thrive in dry shade:
Aegopodium; Carex; Convallaria; Epimedium; Eupatorium; Euphorbia; Euonymus; Gaultheria; Geranium; Hellebore; Heuchera; Hedera; Hypericum; Lamiastrum; Lamium; Liriope; Pachysandra; Salvia and Vinca.
Best wishes with your flower bed!
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