That sounds like a great idea! I'm sure it will come out really pretty! :)
Here's a pretty good pic of intertwined wedding rings, your tattoo artist can use this as a reference :
http://www.weddingservicesonline.com/datas/img/thumb1.jpg
Unfortunately, as i'm sure you have already found out, when I search for what you are asking for, it comes up with actual wedding ring tattoos on your finger.
The easiest thing for you to do is, take the pic from the link I gave you and give it to a tattoo artist or a good friend you know that can draw, this way they have a point of reference. Describe to this person exactly what you want, how you want it to look, etc. If you have a friend or family member do it, take what they draw in to your tattoo artist and have them re-sketch it on transfer paper for your tattoo. If you have a tattoo artist draw it, then you should be good to go.
Dont settle for what you dont want. If something does not look right, you still want more added, or anything else, let this person know. Remember, this tattoo will be on you forever, so make sure it is exactly what you want and how you want it to look.
Good luck! :)