I shot some footage using a Canon DSLR. When I view the footage on my computer or TV, the dark areas contain no grain. However, when I render the project the grain appears in the dark areas. The original footage is 1080/30p I tried rendering both mpeg2 and mpeg4 files but I get the same result. Is there a better way to render to avoid this? It happens with or without color correction.

Sounds like the visible grain is a compression artifact, the grain is there in the footage even if originally you don't see it. Could you try a higher bitrate? if no improvement, using Neat Video would be a fix.