There is a dry ice method that seems to be pretty humane.
https://www.backyardchickens.com/t/259799/non-violent-way-to-kill-a-chicken/10
https://www.backyardchickens.com/t/259799/non-violent-way-to-kill-a-chicken/10
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And IMO, broom stick, decapitation or quick bleed out are faster and far less traumatic to the bird than a slow death by oxygen deprivation.