Baby who can’t be put down

Hello fellow parents, Any advice on how to sleep safely (at night) with a 2 month old baby who can’t be put down? He can only sleep carried upright or chest down on us. Daytime contact nap is fine but night time is really hard especially when we’re tired. If we put him down he’ll sleep max 40-1 hour. If we hold him he’ll sleep 2-3 hours but that means we’ll have to be awake to hold him. Thank you for any tips / advice!