There is federal law limiting what gifts you can give a postman (they are federal employees). You don't want to get him fired, so follow these guidelines from the USPS website. Pay special attention to the last exclusion (NO CASH):
Gifts to Postal Service Employees
While many Postal Service™ customers have traditionally thanked their letter carrier with gifts of cash during the holiday season, this practice puts our employees at risk of violating federal law. The Standards of Ethical Conduct for Employees of the Executive Branch ("Standards"), specifies that Postal Service employees may not accept gifts from outside sources (including Postal Service customers) or gifts given to them because of their official positions. Postal Service employees are also prohibited from soliciting gifts from outside sources.
There are a number of exceptions and exclusions to the general gifts rule. Postal Service employees may accept the following items:
-Snacks and beverages that are not offered as part of a meal.
-Items with little intrinsic value (i.e., greeting cards, plaques, pens, coffee mugs, etc.).
-Perishable items (i.e., flowers, chocolates, cookies, etc.); if the items are clearly worth more than $20, employees should share them with others in the Postal Service workplace.
-Items with a market (retail) value of $20 or less.
-Gifts motivated solely because of a personal relationship.
-Gifts for which the employee has paid market (retail) value.
-Gifts paid for by the Postal Service.
-Postal Service employees may not accept cash - in any amount or form (bills, checks, money orders) - from an outside source.
Edit: I have neveral been a federal employee. I just don't want misguided appreciation to get someone fired for Christmas. It has happened. I think he'd appreciate something he can use on his route more anyway (cookies, cocoa, mug, etc.)