In InDesign you would need to paste the group into a new, frame, properly sized and shaped, and add the stroke to that frame.
In Illustrator you could do it very easy and save it as AI and place it in InDesign as you can add there strokes (several!) to each object, group and layer as group.
depending on the two circles, if they are filled or not, you have several options in InDesign to do what you want.
1. If both circles are filled like that:
you could duplicate the group, apply a stroke and stack the duplicate behind the original group:
2. You could use an effect on the group (in this example I used a green color for the "stroke", that is no stroke at all, but an effect):
The problem with that is:
A. If you later want one of the circles not filled:
B. Exported to PDF and printed the effect will have a smooth edge as an exported PDF/X-4 in Acrobat Pro is showing:
3. And then we have the Pathfinder Add option that will require some steps:
Hope, that helps!