I play better with an open chess board rather than a closed one. What openings are best to persuade one side to trade off a pawn or two to open the game up?
The scotch game is a good option id say
Double KP Openings in general are "open" although there are plenty of exceptions to the "rule" here.
As far as persuading anyone to do anything OTB I'm unclear on the concept here - the best you can do as White is to play openings such as the Kings Gambit, Evans Gambit, Fried Liver Attack, Moller Attack etc and see how your opponent responds. As Black answer 1.e4 with e5 and 1.d4 with d5, to maximize your chances of getting an open game.
Don't worry about how sound all my suggestions are (ie the Moller Attack is theoretically refuted for instance) unless and until your opponents demonstrate that they really know what's wrong with something like the KG or Evans Gambit - in this case, both are genuine gambits with no guarantee you'll ever recover the pawn.
If you are white what is your first move?
e4 will give you more open positions.