I own a small business and used a labor agency several times this year. It is my understanding that I cannot file a MISC 1099 if they are incorporated, which they are. How do I file and report the payments made to them, and ensure they paid employment taxes?

Did the workers work for you or were they actually working for the labor agency?

If they worked for the labor agency, you were merely paying the company to provide labor, thus this is merely a business expesen
And since they were not working for you, but working for the labor company it is the labor company that has the liability to provide unemployment, workers comp and paying the taxes.

If they were merely the book keepers and you were paying the employees yourself, that changes it.

You will claim it as contract labor. I think it's line 11 on Schedule c. They are responsible for paying any employee taxes. You hired the services of a corporation. They account for their income through account receivables. Your proof is the invoice that they billed you and you paid for their services. A corporate tax is return is totally different than an individual Form1040 return.

Agreed. It appears you have NO responsibility for employment or unemployment taxes. It was contract labor.