You were most likely right in saying 'no' straight out.
Coffee is considered organic if no chemical substances were used for its production. This includes herbicides, pesticides, and I believe some fertilizers too. Wikipedia agrees with this.
But even if you're a coffee producer and you're sure you don't use chemical substances and there are no residues in the soil, that's not enough. You have to certify your product and you'll be able to say that your coffee is certified organic. The certification process and agency will depend on where the coffee is grown.
Of course, the certification costs. And some producers might not afford it (thanks to Chris_in_AK for pointing this out).
Since you're only roasting the beans and not producing them, it's not really up to you (you could ask your provider if the beans they're selling you are certified organic). But you could buy beans that are certified organic.