On private property, a driveway or a hard pad is the normal spot and no Town approval attaches to the container itself. That is the answer for most residential jobs in Parker, Colorado, and it is worth stating plainly because the Town's rules are often described less clearly than they deserve.
Public ground is different, and Parker publishes a clear threshold. The Town requires a Street Occupancy Permit to place items in the Town right of way for more than 24 hours, and dumpsters are named in that list alongside storage containers, landscape materials and construction trailers. So a same-day drop and collection in the right of way does not need the permit, while a five-day rental in the right of way does. Applications go through the Town's online permit system, and contractors have to register with Engineering and Public Works before they can use it.
The Town's right of way fee schedule includes lane closure charges and higher peak-hour lane closure charges, which is worth knowing if your container has to sit in a traffic lane rather than a parking lane. Because the published rows carry no effective date, ask Engineering and Public Works for the current figures rather than relying on a number written down elsewhere.
On the collection side, Parker is unusually light. The Town's licensing title covers alcohol, solicitors, security guards, pawnbrokers, massage parlors and a few other trades, and there is no waste or hauler class in it at all. Its health and safety title deals with nuisance and litter, and the duty there falls on the property owner or occupant who lets material pile up or blow onto a neighboring property, not on the company hauling it away. Its two right of way chapters say nothing about containers. In short, there is no Town hauler license to obtain in Parker and no exclusive arrangement to work around.
One caution. Douglas County's own website is not open to automated access at the moment, so nothing is stated here about a county hauler registration or a county facility rule in either direction. Some Colorado counties do license haulers and others do not, and the answer for a neighboring county is not the answer here. The Town of Parker is at 20120 East Mainstreet and takes calls on 303-841-0353 if you want the right of way question settled for your address.