The City of Toronto does not plant trees on private property, but you can contact LEAF (Local Enhancement and Appreciation of Forests). They offer Toronto residents subsidized backyard tree planting.
LEAF is a local not-for-profit organization dedicated to the protection and enhancement of Toronto's urban forest. They offer a number of tree-related programs for Toronto residents. The cost to homeowners ranges between $150 and $200. This price includes a site consultation to select an appropriate species, a 5 to 8 ft native tree and the planting service. Native shrubs are also available.
There are some minimum space requirements that the backyard must meet. For more information on their programs, please call them or visit their website at www.yourleaf.org.
Additionally, there are several City programs that support planting on private property. For more information on these visit Urban Forestry Grants & Incentives.