Over the years and around the world many different designs of Archery target have been used. I'm sure some had red in the centre.
However, today in target archery (e.g. as shot at the Olympics) the target face is standardised and the centre (which is never called the "Bullseye" by archers!) is yellow and is normally referred to as "Gold". An image of a target face can be found at http://upload.wikimedia.org/wikipedia/commons/d/d5/Archery_Target_80cm.svg.
Other target faces do exist; the most noticeably different would be one used for field archery which is all black apart from the centre which is, again, gold.
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