On them is Apple scab. Spray with Copper sulphate or Bordeaux mixture every 2 weeks from when the fruit is set until just before picking. This is a reasonably orgabic control.
If the spots are inside the flesh, then it is Bitter pit and the tree is short of Calcium. Bit hard to treat, But what you may try is boring holes in the soil (I used a big crowbar) and filling them up with lime. Otherwise you are into spraying the flowers with Calcium (if you can get hold of any).