A container on private property, in a driveway or inside a job-site boundary, is the normal arrangement in Solon and that is how almost every job here is served.
The honest position on the written rules is this. Solon's Codified Ordinances are held by an outside publisher that does not serve automated requests, and the only part the city reproduces on its own website is a table of contents for the zoning code. So we take anything that turns on the code straight to the city instead of inventing an answer, and we say so plainly. The Building Department answers those questions on 440-349-6737.
One street rule is on record and worth knowing, because it is the only door of its kind in the Solon streets chapter. The city's permit there covers parading or blocking off a street area, has to be filed not less than five days ahead, and requires the application to designate the area being blocked off. That is a realistic route where a job genuinely closes part of a street, and it is a five-day lead time rather than a same-week one. For anything short of closing a street area, the placement is agreed with the city rather than permitted.
What the city does publish directly is more useful than it sounds, and it points one way. On its own construction debris page, Solon states that its permit application makes disposal of all debris generated from a permitted project the responsibility of the contractor or homeowner, and it goes on to suggest contacting a waste removal service and obtaining a dumpster. A city that tells you in writing to bring in a container is not a city that makes it difficult to place one.
One duty is worth raising before a commercial job. Solon requires a contractor to hold a certificate of registration from the Chief Building Official before performing work in the city, renewed each calendar year, with general liability insurance naming the City of Solon as an additional insured, a sealed bond form and trade licenses from the relevant state board. Whether delivering a container counts as performing work is a question for the city, and the trades it names are building trades. Your account manager raises it with the Building Department where a job makes it matter.
One practical point from the city's own collection rules. A container at the street line is treated as an obstruction risk: the city wants three feet of clearance from parked cars, mailboxes and utility poles, and may remove a receptacle left there more than three days after collection.