What software are you using?
In Photoshop Elements, it is in the layer styles. Mine is 5.0, so I am not sure if yours is different but..
I first have to apply another layer style (say bevel for example) and then click on the sunburst shape in the layer and choose stroke and then specify color, width, etc..
I hope this helps!
By the way, your design is very cute. Please post again when it is done. I'd love to see it - as I'm sure others would as well.