Try Les Ormes for self catering. It is expensive but there may be availability.
Or maybe the Oomeroo hotel (it’s in st Helier right near the beach). I’m not sure what facilities it has just thinking of hotels I know. (I live in jersey).
What’s the budget? Hotel de France might have availability - great pool and spa, the raddison is nice and central as is the Pomme d’or.
Premiere inn has just opened in at Helier too - nothing special but it’s there.
Second prince of Wales in greve de lecq - great breakfasts!
There are a few air bibs too which might be worth a look.
Camping/glamping at the zoo? Pricey but even if for a few nights it could be fun!
Or have you looked at staying In some of the heritage sites? www.jerseyheritage.org/holiday
Family stayed in the radio tower for our wedding a few years ago. Views are amazing.
Off the top of my head other hotels which might have availability (although haven’t been to them are)
Mornington hotel (in st Helier but opposite a lovely park)
Greenhills - in the country will need a hire car
Hotel cristina or Somerville hotel
There are a few guest houses in st aubin (harbour reach www.harbourviewjersey.com/) is meant to be nice.