As much as the vast output of Pueblo pottery makes the contributions of non-Pueblo people to the Native American pottery landscape seem miniscule, there are some excellent, traditional potters out there from other tribes and places. I include Mata Ortiz pottery in this because, like the revival that's been happening in Pueblo pottery, the vast majority of Mata Ortiz pottery can be classed as Mogollon/Mimbres Revival as many of the designs used by the Mata Ortiz potters are interpretations of designs found on ancient pottery shards in the area of Paquimé in Chihuahua, Mexico. In that respect, the original sources of many Mata Ortiz designs can be seen in ancient Pueblo pottery. Mata Ortiz potters also make their pots in the same way the Puebloans do: dig and process their own clay, build their pots by hand using the coil and pinch method, paint, incise and carve decorations by hand and then fire the pots. Mata Ortiz potters do often use modern kilns for firing and they are also blessed with the close proximity of multiple sources of clay, each of a different color.
Historically, it seems cultures across the Americas were producing pottery long before the European invasion began. When the Europeans began to arrive in greater numbers, the population pressure they created forced many tribes to begin migrating westward (although some went north and took refuge among the less aggressive invaders in Canada).
The oldest known ceramics in North America were found in the area of the Savannah River between Georgia and South Carolina. People of the Stallings culture were producing a fiber-tempered pottery used for storage purposes.
It was the Spanish who first brought the horse to the New World and by the early 1700's, horses had been acquired by most tribes as far east as the Mississippi Valley and as far north and west as what is now Washington state. That began the days of the Great Plains and mountain tribes hunting bison on horseback, but it also spelled the end for much of those tribes' fragile pottery.
In my list are Chemehuevi, Cherokee, Choctaw, Winnebago, Wyandot, Lakota Sioux, Jicarilla Apache, Navajo and Tohono O'odham potters. I'm sure there are others out there but these are what I have seen so far...