Here are the Data East machines produced from 1987 to 1994 inclusive.
I have excluded most games with only 1 x game made.
I have however, included the Total Recall, Mad and Ritchie Rich 1 x only machines produced titles)

Hopefully I have included all titles.

Data East had a slow start but started to pick up production quite quickly.

1987-01 Laser War

1988-02 Secret Service  
1988-11 Time Machine  
1988-08 Torpedo Alley

1989-09 Monday Night Football
1989-05 Playboy 35th Anniversary

1990-06 Back to the Future  
1990-04 King Kong (9 x only)
1990-04 Phantom of the Opera
1990-01 Robocop
1990-10 The Simpsons  
1990 Total Recall (1 only)

1991-08 Batman
1991-02 Checkpoint  
1991-09 Star Trek 25th Anniversary
1991-06 Teenage Mutant Ninja Turtles
 
1992-05 Hook  
1992-08 Lethal Weapon 3
1992-12 Star Wars
 
1993-02 Adventures of Rocky and Bullwinkle and Friends    
1993-06 Jurassic Park
1993-10 Last Action Hero Data  
1993-10 Mad (1 x only)
1993-12 Tales from the Crypt
 
1994-07 Guns N' Roses
1994-10 Maverick
1994-07 Richie Rich  
1994-01 The Who's Tommy Pinball Wizard
1994-05 WWF Royal Rumble

Best not to post on this page so that it stays a fact resource page not a discussion page. thanks.