I know you're not looking for brand recommendations, but few subwoofers are designed intentionally to be placed in corners, as you want to. I, too, place my two subwoofers in the front two corners of my room. They are down-firing through a slot. But you will see that many subwoofer users go through heroic efforts - bass traps, EQ, etc., to get good, somewhat flat bass response from corner-placed subwoofers.
That said, my Vandersteen 2Wq subs are specifically designed to perform best when placed in corners. And I have found that they need little if any in the way of EQ or room treatments to compensate for corner placement. I urge you to research this subwoofer and its unique hook-up scheme. I think it might be a good fit for you.