You might get some good results out of a pocket laser projector, like an AnyBeam - that would be in focus at any range, and would have higher resolution than similarly-sized traditional projectors.

You may have trouble getting any projector to work well on a target the size of a business card, though. For the image to be so small, the projector would have to be very close, and they aren't designed for that. The image will be too bright and bleed-y.