On private property, such as your driveway or inside a fenced job site, the City does not require a permit for the container itself. That covers most rentals here.
The right-of-way is different, and Wilsonville's rule is explicit about stored materials. Nobody may occupy the right-of-way, a public easement, or a public utility easement, or store materials in it, without first getting a permit from the City. The permit even has its own name, the Right-of-way and Public Easement Use Permit, and the City Engineer issues it.
The application asks for construction plans and traffic control plans, and it comes with a fee. The City then has 30 days from a complete application to grant it, grant it with conditions, or deny it in writing, with a right of appeal if it is denied. The exemptions in the rule all cover utility work, so none of them helps a container.
Call the Engineering Division at 503-682-4960 to start, or Public Works at 503-682-4092. If you are not sure where the right-of-way line falls on your street, your account manager can help you reach the right City contact before delivery.
One more thing to plan around. Wilsonville provides solid waste collection and disposal through a City franchise, and the City Council sets the rate schedule for it, including drop box service in the sizes most projects use. Because of that, your account manager will confirm how the local rule applies to your address and your project before you book, rather than leaving it to delivery day.
Before you book, confirm with the city that a container can be placed for your job at your address. Rules differ from city to city and they change. Your Prime Dumpster account manager will help you check, and will tell you plainly what your options are here.