There's a game bug where it can still show red even when you have it at the percentage that is right for them. If you look at the % coverage you actually have, what the red bar shows won't necessarily match it. It's just a display bug though, it doesn't effect the animals actual happiness. Just go for getting that % in the target range they desire and don't worry about if it's red or not, as long as they are actually getting "100%" for the Plants rating above the coverage rating, you're golden.
For Zebras, coverage between 0-30% should be what turns it green, which means it should start green before any plants are added. If it's not, you just are experiencing the bug. I started having the coverage getting stuck as red after the 1.02 patch. It's happened less frequently since 1.03, but I still get it once in a while for some habitats.