I've actually found that cats do lower stress (unless they're clawing the furniture).
I spent nearly two years in bed when I was first diagnosed with this autoimmune disease. During that time, my two cats were my constant companions. Having their little warm, purring bodies snuggled up to me made me happy. And feeding them was one of the few things I got out of bed for (and even that was exhausting). They gave me a reason to keep on going even when things were really bleak - I doubt I would have fared so well if not for them. There's a lot to be said for animal companions.