I believe Coopers hawks are rather small and prey mostly on small birds. We have red tail hawks that will take a chicken or small duck. They don't even try with my Muscovy.
I've had eagles take my smaller ducks but leave the Muscovy alone. I'm pretty sure an eagle could take a Muscovy and maybe a goose but it would be a lot of trouble and they look for easy prey. A young eagle might give it a try and injure a goose.
I've not had trouble with coyote. The coyote in my area typically hunt at night. All my birds are in at night. That said coyote are very adaptable. Not sure how or when they hunt in your area. They could definately take a goose. I have donkeys that took care of one coyote that tried to get my birds, but it's not easy to keep birds in the same area as donkeys.
Our biggest issue has been fox. We never had a problem until last year. They seem to hunt at any time. We literally went into the shed for two minutes, the fox was waiting and took a rooster in that little time. I'm not exaggerating, two minutes.
One of the problems we've had with the fox is how fast they learn. We put up 6' welded wire fence for day grazing, the fox figured out how to dig under it very quickly. They also dig very quickly. We should have buried the wire but it was only for day grazing, we thought it would be ok.
The first time we saw the fox go for a Muscovy it didn't win the fight with my beloved Muscovy hen. But it apparently learned how to win the fight and my ducks are no longer safe.
I keep mentioning the Muscovy because they are as large as a small goose and seem to fight off predators in a similar way geese will.
I've since moved and am going to try with geese this year. i haven't had any for many years. I'm setting things up so the donkeys can be in the same pasture as the geese (when the geese are old enough). I hope this works. I'd get a livestock guardian dog but I know myself well enough to realize it would probably become a house dog.