I include a card with coupon code for a small discount, etsy address, and other information when I ship my orders, and there is an etsy setting that when you ship your order, the costumer also get an email with a thank you coupon code.
That's my attempt so far. I have been having repeat costumers, but interesting they never used the coupon codes.
My concern is not really if it is allowed, but if it will be a good strategy for you. If I get a card from a etsy seller I used to buy things, I will feel more awkward than anything.