Lets say both of a person's parents are vampires... would the two create a vampire offspring?
There is some disagreement among vampire mythologies about this, but the consensus is that vampires cannot reproduce as they did when they were human. So the answer would be "no".
But here's why: Vampires are technically dead. Their bodies don't function the same as they did when they were alive, which is why they don't generate body heat and why they can't digest regular food (they absorb blood, they don't digest it). Therefore, it is reasonable to believe that this is the reason they also cannot create a child via the regular sperm/egg method. This also, though, explains why a vampire bite can turn others into a vampire.
Every species on earth has learned how to reproduce. There are even some cases of amphibious creatures literally changing sexes in order to keep the species alive. There's no doubt that vampires developed their inherently reproductive bacteria for this same purpose.
In other words, vampires reproduce through the transfer of this bacteria, most commonly through a bite. If you think about it, this is much faster and easier than a 9-month gestation period and only takes one "living" vampire to reproduce.
That said, there is reason to believe that a vampire male may be able to reproduce old-school style with a human female. It would have to be in this combination because only a human female would be able to carry a living fetus. Most animal species, including humans, can continue to produce sperm all the way through life, and even though a vampire is technically dead, there are some still active elements... I won't get into details here but you can figure it out.
I'm not sure how common this is, I would guess it was exceedingly rare, but I wouldn't bet against this possibility. The child would then be some kind of half-vampire/half-human. How exactly that would work out I'm not sure, but it would most certainly be more human-like with some inner vampire qualities and abilities.