Unlike Java Edition, in Bedrock, non-white carpets can’t be dyed. There is no recipe in the crafting table. Since things like the Minecraft article “Taking Inventory: Carpet“ and Minecraft wikis both say any carpet can be dyed any color, with no mention of it being exclusive to Java Edition, I assume this is a bug.
We're tracking this issue at MCPE-170482, so I will resolve and link this report as a duplicate.
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