A greetings card = two-fold card, crease in the middle. Like this?
Okay, first it was a postcard what I thought you had in mind, but I see now a "greetings card" is not a postcard. I would ask a book printing house, or suchalike. They have the machinery to make the crease, such a simple job really, and if you order a big enough quantity it might even be affordable. Some small business place would most likely be flexible enough to have room in their daily schedule to make these for you.
For convenience it'd be good to look for such a shop near you, allowing you to see yourself the variety of paper qualities they have in stock. Phone catalog Yellow pages should offer the best source for what print houses there are near you. In case they don't have photo-printing quality paper, you might be allowed to bring your own papers which they then cut and fold the way you want it.
Of course, you might consider letting them do the printing too. Ask for samples of their print quality and color accuracy. Costly, perhaps, but worth to ask anyway.
A mother of my childhood friend worked in this kind of smallish book printing house, and they did this kind of jobs in between those books.