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 Orti 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 Pueblos 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 the less nomadic tribes across the Americas were producing pottery 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). The Europeans also brought the horse to the new rold and by the early 1700's, horses were being acquired by most tribes in the Mississippi valley and to the west. That began the days of the Great Plains tribes hunting bison on horseback but it also spelled the end for much of those tribes fragile pottery.
Also in my list are Chemehuevi, Cherokee, Choctaw, Winnebago, 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...