No, they can't. I think Damon from The Vampire Diaries said it best : "Vampires can't procreate... though we love to try." :-)
But also, in Moonlight, Josef said to Mick: "And unless you and Beth figure out a way around the vampire rules of love and procreate... "
During the later part of the Moonlight season, we are told that vampires can't have children and unless Mick and Beth find a way to rewrite the rules, they will never have any. To me that screamed out that they will indeed find a way around it. Now, that could be as easy as Mick haviong viable sperm after his brief stint as a human right before he and Beth got together or there might have been some relatively unknow way of that happening to be revealed in the never filmed season two. I don't think Moonlight would have gone to so much trouble to talk about it and have Mick think he might have fathered a child with a long ago lover only to find he hadn't, if they weren't considering the possibility of having Beth pregnant at some point. It's certainly worth some fan fic!
No. They can't and don't even think they can because of Twilight because every vampire story is different. Like for insinsts the vampires in vthe series Vampire Acdamey or the TV series Angel. In the book series there are 3 types of vampires but in the TV series Angel are only one type, just like most vampire based movies, books, or TV shows. Another one that has more than one type of vampire is the the book series Blue Blood.
