I am curious about the exact identity of this persistently present sunflower. There are many perennial Sunflowers (Helianthus) as well as yellow daisies in other genera that are commonly referred to as sunflowers.
One particularly pleasant perennial sunflower is the Jerusalem Artichoke (Helianthus tuberous) that does double duty as both a robust ornamental and delicious vegetable. A bed of Jerusalem Artichoke would be boon of many blessings, even in a small garden.
Still, if the plant is truly not wanted, persistence with weeding is the key.
It would be good to see a photograph of the bed and the plant, but if we assume that the plant has truly taken over the entire bed, then one can be ruthless in digging with either spade or mattock. Turn up the entire bed, removing any plant tissue that is encountered. This material can be composted or left out until fully desiccated and then used as mulch.
Mulching, amending, and/or replanting the bed will further discourage resprouting. However, even after this effort, it is still quite possible that some additional sprouts will come up. These should be promptly and persistently removed when seen, until the plant is truly no longer present.