Pay parking at hotels has long been a fact of life in downtown Ottawa.
Have you tried the CY in Byward Market? Unless you have business in the immediate area from the downtown Marriott, the Courtyard is in a much better location. That's certainly true for leisure travellers....walking distance to restaurants, pubs, shopping and still nearby other attractions, including Parliment Buildings.
Its a somewhat older hotel, but nicely re-done from its Holiday Inn/Market Square Inn days. Garage parking under the hotel and a full serv restaurant on premises. (If memory serves, the parking is $11 CDN per night.)