Do materials exist that absorb Visible light and emit Near InfraRed light?
Yes, there are some minerals that shows VIS-NIR luminescence here a couple:


Synthetic ruby $\ce{Al2O3:Cr}$
Kyanite ($\ce{Al2SiO5}$)


(Reference here) 

A more sophisticated material is $\ce{LiSrPO4:Eu2+, Pr3+}$ you can read the full article in 11 February 2013 / Vol. 21, No. 3 / OPTICS EXPRESS 3161.

There are also some pigments like egyptian blue or cadmium yellow (CI pigment yellow 37, that is cadmium sulfide) that were also used in the past. Egyptian blue (calcium copper silicate ($\ce{CaCuSi4O10}$))  is safe, other pigments with cadmium are more toxic.

One of the most spread pigment shows VIS-NIR luminescence: Chlorophyll!

Have a look to this site for a nice overview. 



All the luminesce processes have not a high quantum yield, so to record them, most of the times, you have to avoid reflection. Tungsten, halogen lamps and sun emit a lot of NIR radiation so is possible that reflected light overhang the luminescence. When I performed NIR luminescence I used VIS LEDs and a long pass filter at 850 nm.  If you don't have result, first thing you have to try is to remove the ICF (IR-Cut off-Filter) filter from your camera so NIR light can reach the sensor more easily.