Artificial production alone doesn't do the trick. It would have to be low in energy consumption, preferably exothermic. I don't think there is such a reaction with plentifully available material. Otherwise you spend more energy on the basalt than the CO_2 production gave you.

Also, large parts of this planet consist of natural basalt deposits, every area with some current or historic vulcanism has them. E.g. half of Siberia is a huge basalt deposit. Google Siberian Trap. So I do not think artificial production would be necessary.