I presume you know your ship's rotation. In that case,

 // you should probably put this somewhere near the initialization code;
 // no point in assigning it every frame:
 float distance = 10.0; // how much our projectiles will be offseted left and right
 // if your ship's rotation is stored in playerOne.Rotation and expressed in radians:
 projectileOnePosition.x = playerPosition.x + Math.cos(playerOne.Rotation - Math.PI/2) * distance;
 projectileOnePosition.y = playerPosition.y + Math.sin(playerOne.Rotation - Math.PI/2) * distance;
 // for projectileTwo, add ninety degrees, i.e. + Math.PI/2
 // also, it is a good idea to keep PI/2 precalculated as constant

If you are using degrees for rotation (I am not familiar with XNA enough, but this is basic stuff), you can convert them using simple formula Radians = Math.PI * Degrees / 180.0