All during the 60s
The US issued the first postage stamps in 1847.
The short answer would be approximately 1776-1789 or 1777-1789, depending on how you choose to view it. The Articles were drafted in 1776 and approved by the Continental Congress in 1777 but...
On March 3, 1863, the US issued its first postage stamps, they were 3 cents, for a one half ounce letter.
1861-1865