• NEVER attempt a negotiation with over 5 choices without activating the Extra Turn Tavern boost (15 minute only, you NEVER need more)
• Round 1 is ALWAYS alternating supplies/coins. Start with whichever you have the most of, and alternate from there (coin/supply/coin/supply/coin OR supply/coin/supply/coin/supply). Alternately, you can try coin/supply/goods/goods/goods. It can drain your goods faster, but sometimes it can make things go a lot smoother too (via ProudCentaur).
• If you have more than two choices in round 2 that could be either coins or supplys, DO NOT fill them all. Fill as few as possible with coins or supplies so that by the end of round 3 or 4, you'll have them filled correctly. This gives you the maximum amount of attempts to find the correct goods. Example:

Round 1: coin - supply - coin - supply - coin. All turn yellow.

Round 2: supply - coin - goods - goods - goods. Supply and coin turn yellow again.

Round 3: goods - goods - supply - coin - goods. Coin is correct/green, supply is yellow,

Round 4: goods - goods - goods - coin (green) - supply. Supply is now correct/green

• In later levels, sometimes even 4 turns just won't be enough. If you KNOW you can solve the negotiation in one more turn, don't be afraid to spend 10 diamonds for another turn rather than burn even more goods trying all over again. GE pays out diamonds pretty often, and if you're looping like a good forger should, each repeatable quest will pay out diamonds once as well.
• ALWAYS make early guesses with goods from your most numerous down to your least. each guess removes goods from your supply, and your earliest goods guess may have to switch another 2 times or more. 
• Sometimes it's to your advantage to abandon a negotiation early to save goods (close the negotiation window before all turns have been used). Practice and repetition will tell you when this is.