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Double side tape works fine. Make sure you are using the heavy duty stuff (it's grey with red plastic on the outside). I ran two pieces along the entire width of the spoiler. It's definitely stuck on tight and not going anywhere.
Is that the only thing that is CF on the exterior of your car? Show us am image of your whole car please.
Here's an older pic, from back in April of last year. Currently have EMR CF front lip, side skirts, rear lip, trunk (TRD style) spoiler and roof spoiler. VIS CF grill, CF eyelids and tail light covers, CF license plate frame, CF mirror covers and CF door pillars.