I thought the door hanger from SVGCuts new kit B is for Birthday would make a great wine bottle hanger you could tuck a gift card inside the attached box. I scaled all the files down to 85% in ssde and it works out perfectly, the gift card fits with no problem and the hanger looks good on the wine bottle. I cut a a piece of paper 3.715h x 3.640w that I attached the gift card too so you can slide it out easily.
I used some stamps from the July KOTM from Unity that were wine related and added some Tickled with Teal Trendy Twine. The digital paper is from Lori Whitlock's Fresh Air collection.