with a d16a2, the crx(si model) can be relatively quick stock, due to the fact that it weighs almost nothing.
Depending on the year of the civic(i'm assuming 5th gen, 92-95) it's got a d16a6 I believe. Gutless wonder. Little more than 100 horsepower. It it's a hatchback, it has a chance of winning, if the guy doesnt suck at driving, although I know very little about cavaliers. It all comes down to who's the better driver though. You should get a girl with a rx-7 to race him.
But please, keep it legal, take it to the track.