A quick gander looks like you need to have been...
"...convicted, or found not guilty of by reason of insanity (or guilty of conspiracy or attempt to commit)...
--Distribution of, or intent to distribute, a controlled substance... [or]
--Felony involving... Illegal possession of a controlled substance punishable by a maximum term of imprisonment of more than 1 year."
...to be automatically cut on the basis of the background check.
Now, that's HIGHLY snipped and it sure isn't legal advice, but I'm not sure that, from a strictly fingerprint-based CHRS standpoint, you're automatically in trouble here. On the other hand, Intruder is probably on the right track... there are lots of folks out there without ANY criminal record, and there's little incentive to employ someone who does have one.
If it were me (and I mean that most literally--I'm not for a minute suggesting a particular plan of attack), I'd probably seek out someone who makes these sorts of hiring decisions and try to get into a frank discussion. You'd be aiming for someone above the rank-and-file... the HR worker-bees will tell you that "we NEVER hire someone with a drug record," etc, and leave it at that. You're looking for someone who can actually use his or her brain and has the authority to make this kind of call. There's always the chance that being up-front and honest may counter the baggage you're bringing to the party. I'd be working hard to develop a network of people who might be in such a position (my initial instructor had a student who ended up being somebody who knows somebody, etc).