Cannot identify a tree and its berries :(

I just purchased a townhome, and my neighbor has a tree with berries that fall in my backyard. I have two small dogs and just want to make sure that the berries are not poisonous for them. I attached a close-up picture of the tree and the berries, and I am hoping that someone can possibly recognize it. Any help would be great :D

 

Maybe Ligustrum, privet.

 

I think you're absolutely correct! Thanks so much Eric!

 

Leaves look to be alternate, so not privet. Sorry, don't know what it is though.

 

Quite similar to Ilex cornuta except for the black fruits instead of red. So, a black-fruited form of that or a related species producing black fruits.