I'm just a beginner so the following is just a guess:
I think that Áine is often used to represent the name Anne. The dimunitive form of a name is usually made by changing the name's end or adding the suffix "ín." So, my guess would be Áinín.
Please note that you'll find that there are folks here that take strong exception, often to the extent of cringing, to translating names from one language to another. I have a sister named Anne, who likes to be called Annie, so I would be interested also in the proper, if possible, representation of "Annie." I suppose one way of identifying whether "Áine" is a correct representation of "Anne" would be looking in an Irish-language Bible.
Please wait for input/corrections from others, especially if your getting a tatoo.