If you are visiting in July/August, it would be worthwhile making Advanced Dining Reservations (you can book up to 180 days in advance) as when we have been at Disney in August over the past few years, there have been very few "walk-ups" available in the parks.
If you don't like the idea of making reservations so far in advance, then consider eating at "odd" times such as 11:30 for lunch or 16:00 for dinner - more chance of getting a table - or trying the resort hotels (e.g. Contemporary, Grand Floridian or Contemporary if visiting Magic Kingdom). Also worth checking with your hotel concierge (if staying on-site) in the morning for availability for restaurants.
You can also free up some days by booking a couple of Signature Restaurants or Dinner Shows that use two Table Service credits. As noted above, as the Counter Service meals are quite large, you could easily share 2 meals between three of you and therefore keep a couple of credits for days you would not have a Table Service credit.
Maybe have a look through the menus and make a list of which restaurants you would like to try, then try and work these into any planned theme park visits you have.