Shrubs you can grow include: Weeping willow, elms, blackwood (Acacia melanoxylon), Coprosma retusa (looking glass plant) and tree lucerne or Tagasaste. You can also grow leafy vegetables to feed to your goats.
Note that there are some garden plants that are poisonous to goats. Some examples of these are: Azalea, Daphne, fuchsia, foxglove, laurel, rhubarb leaves, green parts of the potato or tomato. If in doubt, get a good book!
Tagasaste has my wholehearted recommendation as a drought-tolerant shrub that can be cut back severely and then will happily regenerate in the absence of rain. Ruminants find it very palatable. We cut and carry it, but you can plant it in fenced hedgerows for direct browsing, provided the animals are kept off it for about the first 2 years.