That will go on your nervs!
Hillbilly gave a 100% correct statement.
If you are prepared to spend a lot of money and to go through stressy situations you may try it.
First you would have to apply for an exit visa for the Cuban person with the Cuban immigration department including a letter of invitation signed by a Dominican or foreign sponsor having a permanent residency in the DR . After completion of that step an application for a sponsored tourist visa must be filed with the Dominican consulate in Havana involving a lot of paperwork. Even in such a case it is unlikely that they will grant him a tourist visa but it is not a 100 % impossible. But I would not advice you to do it.
If you want to know all the details email me.