With multiple domains, I haven't been able to get CardDAV working under SL (Lion is no problem). The basic instructions (single domain) are here.
Additional notes, including links to related bugzilla entries: Ajcody-Apple-Mac-Issues - Zimbra :: Wiki. From comments in those entries, you'll find links to discussions of workarounds. I tried one of them involving setting up a special DNS record (or putting the record into /etc/hosts) but it didn't work. Maybe you'll have better luck.