I have a couple of goats I like to let run around my yard, problem is I have a few flowering plants out there too. The goats seem to target these heavily, I was wondering if there was some way to keep them from eating specific plants/groups of plants? They get all the free choice hay they want at their pen, so I know they're not starving.
Goats are browsers rather than grazers. That means that they prefer to eat woody shoots and stems of trees and shrubs (including your flowering plants) over grasses like hay. In this regard goats are more closely related to deer than to other domestic livestock like sheep or cattle, which are both grazers.
Like Tea Drinker mentioned they also like variety and will try pretty much anything if left to their own devices.
Some goats are immune to electric fences. I usually chase my goats out of the roses and various other plants with a stick. I have also resorted to waving my arms and rather ugly words. I never touch them (well today I whacked the female for the first time) she had just finished off the last of the newly potted plants, in our enclosed anti-goat terrace. They are lovely but the male goat pisses on the children's toys. Yes, he is a goat, not a dog. I have a 3 foot wooden fence and it is just something fun to jump over. I also have a four foot electric fence that deters all other animals but goats.
My advice is to love your goats more than the plants because they will eat all your favorites, perch on everything like parrots, bleat early in the morning and their mating habits are not good morning material.
We have goats on our farm. Larger ones and small, Dwarf Nigerian ones. One things is true about animals in a fence, they'll test the fences. Horse, donkey, pig, goat... they'll test the fence and if the fence has a weakness, they'll likely find it.
We use goat/sheep fence to keep the goats within their fields. This is a woven wire fence with 4" x 4" openings. The woven wire is more expensive than the welded wire but it is considerably more durable. Our goat fence is 4' high and that is certainly sufficient to contain a goat as long as there is nothing nearby upon which it can climb. We utilize electric tape to encourage the larger animals to respect the fence (a horse can put tremendous pressure on fence posts) but the goats tend to be happy with their pasture.
To keep them off of a particular area, I'd think step-in posts with electric netting and a sufficiently powerful solar charger would be a good choice.
A tea of goat dung has been use since before I was a kid that was 65 years ago and my grandmother told me about that and she passed at 87 abut 40 yrs ago they lived and didn't get diseased and the tea helps the plant to thrive. secondly after raising a herd of over a hundred goats I've found that a 39 inch woven wire fence with two strands of barbed wire with a strand of electric wire between them and one half way up on the woven wire does good also if you can rotate them bi-daily and into areas that has some brush that seems to entertain them and they aren't so apt to want to got out as quick.
Goats can absolutely be trained not to eat your garden! Just blow a puff of air at their face for a small infraction and if you really want to deter them from an area just spray them briefly with a hose. I guarantee they'll learn real quick what you don't want them to eat. I don't even have to fence in my goat. I started early taking him on walks when he was 3 months old and now fences are irrelevant. He knows where I am, his home is and so it doesn't matter if he's in the front yard/back yard. That boy is almost never out of my sight and if he does step out of sight just call his name and he comes running.