This may or may not be helpful. And it may not have been this exact course, but some former colleagues did a Coursera on teamwork communications and found it helpful. I was going to take it the next time it was offered as part of my own professional development, but then our organization got sunsetted and life happened.
Anyway, looks like they've got a session just starting up. In case you aren't familiar with them, Coursera courses are usually free to audit; you only pay if you want a certificate or something for whatever reason (sometimes you get less instructor feedback). Something like that might be helpful, but it would require interest, time, and buy-in by all involved or it's not going to be successful. A small team of compensated staff (who genuinely enjoyed working together) is probably more likely to take it seriously than volunteers who may not see the lack of cohesion as a problem.
In addition to the sites already mentioned, my go-to for nonprofit management resources is https://www.propelnonprofits.org/resources/. I'm not affiliated in any way with that firm, I just think highly of their free resources (no idea about their paid services).
Aside from there, you might want to give some thought to how you structure your meetings and disseminate material before the meetings. For example, do you have a detailed agenda that is distributed before the meeting (in addition to any other pertinent materials)? Do people have an opportunity to add items to the agenda?
It's really simple, but we maintain a Google Sheet where anyone is free to suggest items to discuss so that the agenda isn't always top-down. Each row is a suggestion along with a level of urgency, as well as a notes column. Sometimes people have very different ideas about what's important to discuss and it's helpful to give people an opportunity to collaborate on the agenda before the meeting even starts.
Also, if you're not already doing this, put all of the easy items on the agenda first (e.g., approving the previous meeting's minutes). If there are items that are going to be controversial, save those items for last. On the agenda, allocate a predetermined amount of time for each subject and if you haven't been able to reach a resolution, then offer to table it for the next meeting and/or "take it offline" (i.e., discussion continues afterward between just a subset). Depending on the item, that may or may not be appropriate, but sometimes it's easier to put out fires outside the context of a formal meeting if it's just one or two people who are concerned and the item doesn't require a full vote to resolve. A more formal way of accomplishing the same thing is to refer the item to a committee but sounds like you may not have that level of complexity.
On the agenda, after the schedule, list any necessary action items (e.g., approving last meeting's minutes, approve/review next year's budget, etc). It sometimes helps to motivate the discussion if there are clear objectives for the meeting, rather than simply discussing things.
I'll just close with one final thought, FWIW: if you have individuals who don't have the professional capacity to serve on the board, then you and they might want to reconsider their role. They (and you) may be happier as volunteers rather than board members. Those discussions are hard to have and there's a chance that things will go south (e.g., they quit altogether), but as a last resort it may be necessary. I'm not saying start from that position, but give some thought as to whether it's helpful to have them involved as board members if things don't improve. There's nothing necessarily wrong with them, but sometimes it's just not a good fit.