Near-infrared ink (as posted by an AC) sounds like the most plausible approach. In the range 700-750 nm, the sensitivity for light is less than 1% of the peak sensitivity. You would need (1) a proper long-wavelength-pass filter, (2) ink that absorbs only in this wavelength range, and (3) an illumination source that is heavy in this wavelength area (e.g. halogen/incandescent lights).
For the naked eye, the ink would appear as a very pale cyan color. With a proper filter, everything would look very dark due to the filter removing 99% of the visible light, but the ink would show up with much more contrast. Effective long-pass filters do exist, e.g. Schott RG695 or RG715 for a 695 or 715 nm cut-off, respectively. There are plenty of suitable dyes. Probably you would want to have this filter only on one eye, otherwise the world around you might appear very dark.
The other theories that have been posted here make no sense.
Frequency-doubling needs extremely high intensities (like a high-power or focused low-power laser beam), which would render you blind. Moreeover, frequency-doubling requires proper phase matching, which boils down to the requirement of an exact combination of angle and wavelength.
Polarizers: it is not possible to turn unpolarized light into polarized light without throwing away half of the light. Once the light is polarized, the polarization direction can be manipulated with optically active materials, though.
A high-refractive index coating would not only change at the Brewster angle, it would make the cards much more glossy as seen from any angle. It is not possible to make the refractive index change dramatically within a short wavelength range without changing the absorption as well, so the glossiness would appear in visible light as well.
A phosphor coating would not work for several reasons: phosphors do not emit the phosphorence in the same direction as the absorbed radiation; they always convert from short wavelengths to long wavelengths, and the phosphorence light would be completely out of focus.