You could do a search on anti inflammatory diet or foods. I find that what I eat or do not eat is the main thing to keep inflammation down. In terms of supplements there are some that are very anti inflammatory but then they thin the blood. Like Omega 3's or NAC. If you tend to have thin blood you might bleed more easily. But I think most of the time the coughing up of blood is more from inflammation or infection. You may have to experiment if you are up for that. I started taking NAC recently and so far I am only noticing good effects from it. I just take it every other day and only 600 mg but that seems to be enough for me. And I think that the vitamin K2 has helped with my tendency to have thin blood.