It's absoultely possible to eat healthy on a coupon budget. There are a lot of coupons that save on vegan hamburgers, frozen non-meat products, almond milks, granola, low calorie products, buy this product get money off your produce.
The key is to find a newspaper that is going to have all the inserts in them. For example, I live in southern california and my local newspaper only gives me one insert and it usually has coupons only for cleaning products. So I found that the LA times gives all the inserts in my region and now I get anywhere from 3-5 inserts every sunday. If you look at www.sundaycouponpreview.com, it lists all the coupons that are going to be released that sunday. Just a heplful site to see if you want to purchase the paper that weekend for specific coupons.