No way I would do that.
Here's why - Years ago I had a boutique who wanted exclusivity. They were good buyers and I wanted to make them happy but they wanted to be the only shop in Minnesota that could sell my items. I thought about it and then told them no, I don't offer exclusivity.
Two weeks after they had asked for exclusivity one of the USA's top modern art museums, The Walker Art Center in Minneapolis, began to buy from me for their gift shop. The items sold so well at the Walker Shop they started to invite me to participate in different events at the museum and sell my items during those events. The exposure I got from the Walker lead to magazine features, tons of boutique orders, etc. and my business really took off.
If I would have agreed to the exclusivity with that one boutique I would have never been able to sell to the Walker.
The boutique continued to order from me even though I denied exclusivity.
IMO, here's what you need to remember -
Obviously your items are good sellers for that customer. They would be shooting themselves in the foot if they stop doing business with you if you don't offer exclusivity to them.
You could offer custom colors or something like that as an alternative if they insist.