This was easy in the 70s and 80s
Pick from Bob’s, Beggs or Beeline (just realised the alliteration for the first time by the way)
In fact a poster on here went by the name of beeline before he went all cosmopolitan
All gone now - phukin tories
Coatham Coaches have coaches up to 72 seats.
Saturdays is obviously a busy day for day trips with coach companies.
Commercial Coaches in Middlesbrough have 53 seaters (old family business, but no longer connected, just in case you ask for special discounts)
It might easier to get 2 smaller coaches as the size you want is very big. It also gives flexibility to have 2, by of course its a bit more expensive.
From which direction are you planning to drive in from - say Stockton, Yarm or Redcar or Acklam?