Most video cards can do composite sync if you ask. The driver doesn't always expose the option in an easy to find way, though. You also often have control over the sync polarity. PC convention is to output composite sync on the horizontal sync line.
If you can only get separate, you can combine them externally. Simply connecting the two sync outputs from the PC together is not really recommended, though it will often work. "Proper" composite sync is the exclusive OR of the two, but something that usually works can be produced using a couple resistors (which are often already present on the PC side, hence why connecting the two together often works).