In order to be able to obtain a Canadian permanent residency a Canadian citizen can sponsor you for permanent residency. To determine eligibility you can look at the CIC page, which states:
You can apply to sponsor your spouse, common-law or conjugal partner, or dependent children to immigrate to Canada. It does not matter if they live in or outside Canada. If they live in Canada, they do not need to have legal status to be sponsored.
The question becomes whether or not you will qualify as a common-law or conjugal partner. For that you can look at help center for definitions:
You may apply to sponsor a common-law partner, of the opposite sex or the same sex. If so, you have to prove you have been living with your partner for at least 12 consecutive months in a relationship like a marriage.
A person outside Canada who has had a binding relationship with a sponsor for at least one year but could not live with their partner. The term refers to both opposite-sex and same-sex relationships.
So if you can prove these should be able to get a sponsorship for Canadian Permanent Residency.