I don't have a lot of experience with canker, but that doesn't look like canker to me. Those bumps on the green cane look like scale. I've used Volck oil to control scale. It literally drowns the insects. I've heard that Pam cooking spray works just as well and costs much less, but I've only used it a couple of times and couldn't tell whether it really worked as well or had been sprayed on plants that may have still displayed residual damage but no longer had living scale insects.
There's something else that could be killing the canes. You're growing the rose in a container. Is it possible that your potting medium is too wet?
