The "what would make this deal work?" button is simply a shortcut: it sets up a trade that the AI will accept, so you don't have to click the "Propose Trade" button a hundred times with different values. That auto-deal is very close to optimal, but you can freely tweak the deal until it is more convenient – as long as the value to the AI remains roughly the same. (There are a few caveats, of course: you can't trade cities unless it's a surrender deal, they may dislike you enough that you can't get Open Borders or Defensive Pact for love or money, etc.)
The AI will accept a deal of lower value, but not by much. If you can trade Gold, not just Gold Per Turn (such as if you have a Declaration of Friendship), then you can usually shave ~10 Gold off of the deal after you ask the AI "what would make this deal work?" You can't shave off much more than that; since most resources are worth more than 10 Gold, this means that if you can't trade actual Gold, you can't improve the trade at all because you would be reducing the value of the trade by more than 10 Gold. You can, however, change the trade, as long as the AI values your new offer about the same. So if you'd prefer to trade strategic resources or Gold Per Turn rather than luxury resources, you can swap the trade around. The tricky bit here is that the value of strategic resources changes over the course of the game – in the late game, the AI doesn't offer much for Horses, for instance. (But they'll still ask for horses, because the AI won't ask for more than 5 of any given strategic resource and, when you auto-deal, asks for resources rather than money.)
Unfortunately, I don't have any hard-and-fast numbers on how much you can trade each item for; the value you get from the trade will depend on how much the other guy likes you, what you're trading for, and whether you're asking to buy the last of a given good. (The AI won't offer you more for the last of your goods, though.) An example: typically, you can get 7 Gold Per Turn for a Luxury Good if the other civilization is friendly, and closer to 3 or 4 Gold Per Turn for the same item if they don't like you. Newly-met civilizations will buy a Luxury Good for 5 Gold Per Turn.