In Breaking Dawn, it's shown that vampire males can impregnate human females. Do vampire females still have working reproductive systems? Are vampire males and females able to produce vampire babies?
Stephanie Meyer has commented on this - vampires bodies are unchanging, so a female vampire will never ovulate. Without ovulation, there can be no pregnancy. Even if there was a viable egg at the time of the transformation, the egg would likely become impermeable to sperm, similar to how Bella's amniotic sac was hardened like vampire skin.
It is questionable, then, that male vampires can continue to create sperm. We do, however have evidence that they can - the 'father' of the non-Nessie half-vamp who is brought in at the end of the books is indicated to have been creating half-vamps for a long while, in secret.
They are not able to, as is evidence from previous books. If they were, then it's safe to say that Carlisle and Esme Cullen would have had a baby. Also, Rosalina is quite upset that she can't have babies, leading to a large conflict in Breaking Dawn.
I believe it was explained that vampire females don't go through a menstrual cycle, as their bodies are immutable.
Meyer specifically addressed this point in an FAQ on her official website. Apologies for the length of the quote but it's all moderately relevant.
In brief, female vampires cannot become pregnant. Male vampires are capable of sustaining an erection and impregnating human females due to the presence of "venom" suffusing their cells.
Vampires and pregnancy: when did that idea occur to you? How does that work?
I was always very careful when I answered the “Can vampires have babies?” question, because I didn’t want to say anything incorrect, but I also didn’t want to make the future super-obvious. I focused my answers on the female half of the equation—female vampires cannot have children because their bodies no longer change in any aspect. There is no changing cycle to begin with, and their bodies couldn’t expand to fit a growing child, either. I purposely evaded answering the question, “Can a male vampire get a human female pregnant?” to preserve a tiny bit of surprise in the last book. There were many statements on this subject purported to have come from me, but I never made those comments because, obviously, I knew where this was going.
Vampires are physically similar enough to their human origins to pass as humans under some circumstances (like cloudy days) ... A fluid similar to the venom in their mouths works as a lubricant between the cells, which makes movement possible (note: this fluid is very flammable). ... The normal reactions of arousal are still present in vampires, made possible by venom-related fluids that cause tissues to react similarly as they do to an influx of blood. Like with vampire skin—which looks similar to human skin and has the same basic function—fluids closely related to seminal fluids still exist in male vampires, which carry genetic information and are capable of bonding with a human ovum.
Among humans, some pathogens cross the placenta and affect the fetus while others do not. The outcome of the vampiric conversion of a pregnant woman would probably depend on whether or not the entity responsible for the infection does so. If it does, the fetus should be sustained by the infection quite as well as the woman would be. The fetus might or might not ever be born, but there is no reason to expect a miscarriage. If pregnancy progresses, the infant should be a vampire also. If the infection does not cross the placenta, a female vampire, almost certainly non-breathing, would be unable to support a still-human fetus. It would die, and, one hopes, miscarry promptly.