From ODFW:
Paddle craft and other non-motorized vessels 10 feet and over
Permits for non-motorized craft (canoe, kayak, drift boat, etc.) cost $5. This applies to both resident and nonresident boaters.
Buy: Paddle craft permits can be purchased at ODFW license sales agents, ODFW offices that sell licenses, the Marine Board office in Salem and at Marine Board dealers. A $2 agent applies for ODFW channels.
About paddle craft permits
If a permit is purchased online, print the permit and enclose the permit in a zip-lock bag to protect it from water damage.
If you want to purchase a Tyvek tag permit, you can order one from the Marine Board through the mail. (pdf)
My two cents:
So, you can buy an invasive species permit any place that sells fishing licenses. Also most kayak and canoe stores sell them as well. I usually but the Tyvek tag (tough, colorful, waterproof paper) at Next Adventure in Portland, however one year I did buy the permit from Dick's.