As the PPs have said, getting dining reservations at DLR is nothing like trying to get them for WDW. The dining system rolls somewhere between midnight and 7:00 am (when the phone lines open up), but it's not really critical to be online right when the system rolls. If you get online on the 60-day mark and something shows as unavailable or no times are available, it's much more likely that they've not yet loaded it into the system (opposed to already being fully booked). Just keep checking back and they'll get loaded (sometimes it takes a few days to weeks, but it eventually shows up). Sometimes some special dining events (usually one-offs) fill up pretty quickly, but regular reservations tend to be available for quite a while.
Also note that dining reservations open up one day at a time, so if you did go to make reservations on your 60-day mark, you'd need to check in sequential days for the length of your trip. They don't have the "length of stay" or "+10" that WDW offers to onsite guests.