How can I pickpocket only some of the gold?

Yes you can! You just need to place Paralysis potions in their pockets. After they recover and try to get up quickly pickpocket the gold. It will still say 0% chance but they won't notice it gone and will remain neutral.

You can't select just part of a stack of gold coins. This way, you could rob people of 2000g with just stealing 100 at a time. What I did was I used perks in the pickpocketing tree, potions of pickpocketing and various items. And that increased my chance of success quite a lot.

Also, I think it was a bug but whenever I would access somebody's 'pockets' and gold was the first item, the chance of success was 20%. If I rolled over a couple more items with my mouse and returned on the gold, I'd have 0% chance. So I ended up not using my mouse at all and pressing 'e' to access the character's pocket and 'e' again to loot the gold, at 20% chance.