Are the objects in question three-dimensional? And if so, is the player able to see them from multiple angles?
If so, I know of three good options offhand:
The first option is to simply use the “CommonFilters” module, which includes a “Cartoon Ink” shader.
The second option is to duplicate the object, scale it up a bit (or better yet, expand its vertices in the direction of their normals), then render it inside out (by flipping its “winding order”, likely done by applying a CullFaceAttrib.). You may want to colourise it somewhat in one way or another, depending on your purposes–for a black outline, simply setting its colour-scale to zero (aside from the alpha-value) should do it in most cases, I think.
The third option is to use a custom shader. There are a few ways that such a feature might be implemented in a shader; one method is shown in the “advanced” “cartoon-shader” sample-application, I believe.