so my player has a weapon that per hit deals 1d6 of poison damage, now he picked up the poisoner feat which once his weapon is coated in this new potent poison it deals 2d8 poison damage, so my question is, do they get the initial 1d6 poison damage and then the additional 2d8 on top of that or would the 2d8 override the smaller 1d6?

In general, dnd is additive. It depends on the context, but since the player has a poison weapon, and then coats it in more poison, I would say it stacks. 1d6 poison from the sword, and then 2d8 from the poison. This is both fair, and realistic. But do keep in mind, you're the dm. You're ruling is superior to anything else.

They should be able to stack the d6 and the 2d8, I believe, unless there is something in the wording of either the weapon or the Poisoner feat that indicates they shouldn’t. (Generally, only features with the same name don’t stack -unless they specifically say they do.)

The poison is from different damage source and therefore should stack.

Yes, they add together.

But no to adding poison two times to the same weapon.