The problem is, you'll have a hell of a job finding something to kill them that won't harm bee's. Most insecticide works in the same way, by 'suffocating' the insects by blocking their ventricles, or by breaking down their outer shell. The problem with Ficam, and indeed ant powder/diatom, is that they leave a residue behind that stays active for some time. If you can guarantee the bees won't get in the coop, then it should be ok. If you can't though, I wouldn't chance it as there is a high probability the bee will collect said residue, and take it back to the hive with them, further spreading it. Ficam is incredibly potent for it's quantity, whereas ant powder/diatom would take a considerably more in order to have negative effects.
You could try neem oil, mixed with a few other choice 'organic' compounds, such as nicotine. It won't be nearly as effective, but if you can get on top of the breeding cycle, you can crack them.
I only went with Ficam because I got lazy and it got out of control. I was keeping them in check prior to that a mix of neem, ant powder and diatom.
Can you not put a net over the coop/run to keep the bees out?
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