Water always gets inside my Verizon NID box after a heavy rainfall and my fios service does not work. Verizon keeps on changing the box but quite frankly I think I need to waterproof the NID box. Does anyone know where I can buy a box to cover this Verizon NID box so it doesn't get wet?

I used to work at AT&T where we designed NID boxes. Unfortunately back in those days Bell Atlantic (now Verizon) went with a competitor's box (Keptel, if memory serves) instead of ours.

The box is designed to keep normal rain water out, but it's not water proof - if it's sitting in a puddle of water then water will definitely get in. Do you know how the water is getting in? Assuming the NID is sufficiently above grade so as to not acually end up in standing water my suggestion would be to fashion some sort of protective shroud or covering for it to divert rain. But you're never going to get it totally water proof.

I bet they have old ones in their dumpster. I used to dumpster dive at the Local Cable company and get old boxes, cables, filters.
I would ask one of the local repairmen, or installer on the street, may be able to direct you easier than the voice prompts on getting a replacement cover?