I think you can apply for NEXUS, though the requirements are ambiguous.
Prior to 2012 all NEXUS applicants, regardless of citizenship, had to be resident in Canada or the USA for the prior 3 years. In 2012 the residence requirement was eliminated entirely for Canada and US citizens, and the 3 year requirement was done away with for "certain permanent residents".
Unfortunately I can find no authoritative reference for who is a "certain permanent resident", but I believe the 3 year requirement was in fact eliminated for everyone and replaced with simpler requirement that the permanent resident actually live in the country where they have residence (for a Canadian PR in particular it is possible to live outside Canada for an extended period without losing the status; for a US PR not so much). I believe this because I know the 2012 changes were meant to align NEXUS qualifications with US Global Entry qualifications, and GE has no 3 year requirement.
In any case, lacking more authoritative information, it might be worth just applying for NEXUS to see if you are a "certain permanent resident" since you can't lose much beyond the $50 application fee by doing so. I suspect you'll need to provide documentation showing that you actually reside in Canada, but the fact that you've lived there for less than 3 years won't be a bar. As a Canadian resident you have no choice but NEXUS in any case, so it is that or nothing.