The question has a hidden assumption: that the technology has no problems and it's merely the faculty that need to be convinced. Having used a few different learning management systems (Canvas, Moodle, Blackboard, homegrown stuff), I can tell you that this is rarely true.
The people resistant to change are probably resisting because they've seen different incarnations of this technology come and go, and find it annoying to have to keep learning a new system that doesn't present any significant advantages over what they're doing. The significant part is important. There's a cost to making a change, so the new system can't just be as good.
So I'll add to Chris's excellent suggestions as follows:
make it seamless not just to import, but to export easily. In the world of online software, it's important not to have things be gated. I want assurances that if your new system goes away tomorrow, to be replaced by the next new system, that I can easily transfer material from the old system to the new with a few clicks.
demonstrate why this new system isn't going away in a year to be replaced by something else. How you do that is up to you and depends on the system you're pushing.
Bottom line: the perceived attitude in the question is that the faculty are at fault for not adopting new technology, but the truth is that most new tech is crappy and short-lived, and it's natural to want to wait things out. So you have convince people that the new approach is not crappy and will last.