So would, "... níl cóta amháin agam," not work here? I feel like I'm probably overlooking some rule.
Yes, that would work there. In fact, the translation above is for “any coat” rather than for “one coat” — níl aon chóta amháin agam would have been better for a translation with aon.
Thank you, I thought that was the case. I'll report it next time I see it.