Stiff and chuckle don't go together. I've never heard the words together myself. If I were trying to interpret or understand this ("They had a stiff chuckle") I would think you were trying to say that they were making a half-suppressed chuckle. The verb to use in this case would be "titter". "They tittered" or qualify it as in, "They quietly tittered" or "They loudly tittered". If you want to use the word, 'chuckle', you could say "They softly/quietly chuckled" or use 'loudly' instead of 'quietly' if that's the case. Also, 'chuckle' (or 'titter') aren't words often used in conversation. Their place is more in writing. In conversation you'd usually use 'laugh' in some form and qualify it perhaps, or you'd use some idiomatic expression.

It is ok. Interesting that you use the present tense, but could be done. I chuckle stiffly at the use of present tense. I chortle. I chuckle without reservation. I chuckle insanely. I barely supress a stiff chuckle.

chuckles stiffly is fine :)

I think "to scoff" or "to snort" may be the closest way to describe it. Sure, "chuckle stiffly" is grammatically correct but it does indeed sound a bit weird. But there's no law against using it that way. If it's a stronger reaction, you could also maybe say something like "she choked back a [...]", and fill in the blank with "laugh" (maybe absurdly annoying), "cry" (as in shout), or "rebuke". But it depends on the message you're trying to convey.