Add a Second Stroke

Unfortunately, you cannot apply a filter or an effect to just the stroke of an object. You could draw the stroke separately, but then you'd have to worry about grouping the two objects. Instead, with the object selected, use the flyout menu in the Appearance palette (Window>Appearance) to choose Add New Stroke. Click on the new stroke to highlight it in the Appearance palette, change its color using either the Color palette or the Swatches palette, and change its Weight by going to Window>Stroke. Then go the Effect menu and pick an effect. That way, if you change the size of the original object, this second stroke will automatically change, too.