The genuineness of the relationship isn't what determines the success of a conjugal application. Naturally, if the relationship isn't real, no application would be approved, so the genuineness is just the starting point. Once the officer has determined your relationship is genuine, he will move on to whether you are conjugal partners.
For a conjugal application to be successful, there needs to be some external barrier (usually immigration/legal) keeping you from living together or seeing each other. It has to be something you both have no control over - things like lack of money to travel, or not enough leave from your job, or the need to attend classes will not qualify since you have control those things.
For example, let's say your partner was unable to get a visa to visit you in Canada and you were unable to get a visa to visit them in their country and the two of you couldn't get visas to live/get married in a third country. Then you can expect a conjugal application to succeed.
However, in your case you're saying that the two of you can relatively easily travel to see each other. Therefore, your conjugal application will not succeed. You will have to get married (In Canada or another country where same-sex marriages are legal), or live together for a year and become common law.
