This is my Zombie chord chart by the Cranberries. I used to LOVE playing this song with my band. It"s a pretty simple song because the chord progression is so repetitive. The biggest thing to focus on with this song is dynamics - learning when to play soft and when to play loud.

Since this is a rock song, I would go with all down eighth notes strumming. Sometimes, for dynamic purposes we might do whole note strumming where we strum once on the chord and let it ring for the entire measure. Take a listen to the song to see if you can hear where these transitions take place.