Have checked the favourite days out in Cheshire site, which is usually the first port of call but nothing there at the minute. Would you consider Knowsley safari park instead? The Rhino enclosure there is the same size as the whole of Chester Zoo! There is also a sea lion show.
I have a half price family admission voucher for Knowsley knocking around here somewhere (Thanks Hyundai ) and will be happy to send it to you if you pm me your postal details.