Antiques Dealer: How do I get more Trade Coins and Gemstones?

If you see something you really want, but you don't have enough Trade Coins, you can buy additional Trade Coins for Diamonds. Open the Antiques Dealer from your city and click the + sign next to your Trade Coins amount to buy more.

Gemstones, however, can only be earned by parting ways with your rare inventory items, and can't be purchased for Diamonds.