There would be no immigration record for that time period, but you might want search Naturalization records in New York State if David York or member of his family did get Naturalized. These can be a great source of information.
For a marriage in 1848, you would have to look in District Registers for that period. You need to have an idea of where they lived and what religion they were? Catholic? Protestant? Methodists? Quaker?
During that time period, almost all marriages were religious, and the marriage records have little information, such as bride, groom, 2 witnesses and a clergyman.
Did you search the 1861 census of Ontario for this couple? Which county did they live in ? What was their religious affiliation?
There are two David York in the counties of Lennox and Addington, so you might want to post your query there instead of in York County.