No to a drown circle
Yes to a text object formatted to show a "circle" char.
You could have a duplicate layout one with a red circle and one with a green circle and then change layouts when you want to change colour.
You can also set up a calculation that returns a "container" type that references different container fields--each holding a different color circle or even can be empty to make the circle disappear. Since you may want this circle to circle something, this approach may or may not work for you depending on what you want and how you've designed your layout.
There are a few ways to do this.
1. You could use hidden tab control with 2 panels. One with a red circle the other green. Then you can use Go to Object to go the the panel that you want ( once you have names the objects ). If using FMP10 or 11 you can use a script trigger to go to the panel that you want when it meets your criteria. If not then you can go to it when going to that layout via a script.
2. You can use a 1 line portal and using "visiblilty trick" you can hide the object. This can be used to hide the circle. Do a search for visibility and filemaker and you should come across some posts. In FMP11, this is much easier with filtered portals as no additional relationships are needed.
3. As Daniele pointed out, if you use a text character that looks like a circle ( try wingdings, webdings, etc ). You can use conditional formatting to change the color.
Also please state your version.