At the smaller branch of "Labarotorio Clinica Puerto Plata" laboratory in Sosua (3 day wait for results) or at their bigger lab in Puerto Plata ( get results later in the same day )
Decent service, myself and family got tested and subsequently retested at both branches.
I don't have phone numbers handy as my wife made appointments but if you google the name , their hours and phone numbers come up.
As mentioned if you are willing to pay for the test you can get one from some of the private labs. Usually not a PCR test. if you wish to get a PCR swab test and you have a cedula you can go to the govt. labs and some hospitals in Puerto Plata and wait in line with the masses. You will probably need a doctor's prescription requesting the test. Best to call first or check the websites for a list of requirements. Usually an appointment is needed. Some public/private labs only offer testing in your own house usually for a fee to be paid online as cash at the door generally is not accepted.
There is information on testing scattered around DR1 but no easy to find sticky thread as been created putting all of the relevant info in one convenient place. Contacting a doctor or the public health ministry might get you the current info. Some users on this site are quite knowledgeable on the subject and they may speak up or provide a link to where they have posted the info before.
Public Health: 1-809-686-9140 & 809-200-4091 8am - 8pm
After hours: 1-829-542-7009 8pm-8am
I thought Referencia Lab in POP was certified to do PCR tests early on. Being a private. lab, I doubt. they won’t take a private paying customer. And they do it in your home. See https://www.labreferencia.com/