Empty Nursery barn (Click here for this explanation)
One black stallion foal
1. Put one ready calf or foal in empty nursery barn to make it ready (use move function to move ready animal or else it will harvest it instead of moving it)
2. Now place your Black stallion Foal in ready nursery barn.
3. Take out the Foal or calf you originally placed in the nursery to make it ready.
4. Tend or harvest nursery Barn with just the black stallion foal in it.
If you have more then one black stallion foal, do not put them all together in nursery barn. It will reduce your chances of growing up Black stallion and will increase chances of getting you another adult animal from your nursery barn. Also by just putting one Black stallion foal in barn, it will be much easier since you don't have to move many animals in and out of nursery barn so you can take more chances to grow up Black stallion.
Some people reported if you sell your old Nursery barn and make new one and do above process you will get an adult Black stallion in no time. You do not need to sell your nursery barn to buy another one. As long as your nursery barn is complete you can start a new one, I have four barns already.
UPDATE FROM ZYNGA CUSTOMER HELP WEBSITE: