I'd focus on Return On Time Investment (ROTI) and making it as little effort as possible for them.
Rather than convincing them of the benefits, you need to address their concerns. The classic "if this then this" quote. => "If I address your concerns, until you are happy, then will you allow me to implement this?" Then if they still have concerns then go to other managers.
You don't even have to call it devops, dumb it down and say what you want to do to one system and see if that works, if one works, then move on to the next and before you know it you'll be a devops culture without actually knowing it. :)
Could also have a read through the internet to see if other people also have concerns about devops and how they were handled.
Hope this helps.