I know of mini herefords and mini scottish highlands.

Dexters are small black cattle that any one can handle.

Vietnamese Pot Belly pigs have been around for many decades. The key to keeping them small is food that is high in nutrition and low in carobs and fat. They now make a food especially for them. They are very loving, smart and love to ride in a car. Some love kids while others can get nippy. They are easily trained and house broken. Some even potty train them to use the toilet and flushing afterwards. They can be underfoot like a terrier (very attention needy).

They have other breeds but I only have experience with Pot Belly pigs.

I used to raise pot belly pigs. This time around I'm going with guinea hogs. Easy to keep, safer around kids, easy to fence in or pen, easy to butcher.

My potbellies are just over 100 pounds.
That, is still a tiny pig.
And dexters can be difficult to handle, they still weight 600-1000 pounds... and come in 3 colours not just black. They can kick too!