On the right heading towards Puerto Plata passing through Los Charamicos (near Delancer), there is a small moto repuestos place.
They have inner tubes, if that's what you're looking for, although the selection is limited.
If you can't get to PP as suggested above, there's a new guy fixing / patching moto tires right by La Pulga on Pedro Clisante.
How long the patches work (or if he has any stock) I know not, but the cost is cheap for a patch...