Infrared LEDs with minimal RED glow
The human eye response stops at around 700nm to 750nm, you might be picking up a small amount of red because there are still a few photons in the red range produced and the eye is really sensitive to them in the dark. (its been theorized that the eye can be used as an individual photon detector.) 


Source: http://hyperphysics.phy-astr.gsu.edu/hbase/vision/colcon.html

My suggestion would be to get a high pass optical filter at 850nm or 900nm and see if that solves your problem. And you can't stop all of the photons from getting through, only attenuate them. Maybe an IR laser, that transmitted at 850nm or 900nm might work also as the bandwidth is much smaller than an LED and will have less (almost no) 'leakage' into the 700-750nm range.