If you live within the city limits of Puyallup you can apply with the Puyallup Police Department.
If you live in the unincorporated area of the county, you must apply with South Sound 911 Records in Tacoma. All of SS911 services are made online. Here is a link for SS911 CPL information: Concealed Pistol Licenses - South Sound 911
Non-Washington residents may apply at any local law enforcement agency in Washington State.