For any library, making sure the library director understands the importance of all staff learning and understanding the library's role in coding is the first "buy-in" necessary. Then it's a matter of allowing time and repeated opportunity for exposure. Can everyone on staff communicate the "why" your library is coding?
In terms of staff development activities, your options will greatly depend on the size of your library and established staff involvement of programs. See "Getting Your Feet Wet" under Basic Concepts of Coding for ideas.
For a larger library that has access to equipment, devices with apps, and possibly coding gadgets, training might take place in an open house session. Consider planning this style of event with a beginning session that gives an overview of all the resources that are available for staff to try. During the event, plan stations to be set up with the equipment and instructions necessary so that any staff member can begin the activity on their own. For libraries without lots of equipment or space, consider hosting a smaller training with a single activity, or an unplugged activity that does not need access to technology. Or, consider pooling your resources with libraries in your system for a multi-library staff training event.
Offering short coding activities can be an excellent way to encourage board members to take a more active role in promoting library programs. Giving board members 15 minutes to work on an activity in the Scratch Jr. app on library iPads, or to participate in an unplugged activity such as Table Top Coding using a checkerboard can help build board comradery while also making a case for coding and libraries.