Firstly, if you hover your mouse over an item (or click on an item to see its details) and it says it is a "gift," then you can use it to increase affection. Though I do not know if there are any variations of the gifts yet, the main one to buy is just called "Trinkets"; the icon for it looks like a gold necklace with some rings around it. It costs 2500 gold to buy, and it gives 25 relation.