Unfortunately there is no current Zapier zap for Google My Business posts. However, you can auto-post to Google My Business using OneUp.
Many people are looking to post to their Facebook page, and then have that post automatically go to Google My Business posts as well.
First, you must go to RSS.app (which is free) and create an RSS feed of the social account you want to post FROM.
Then copy your RSS feed URL
After, go to OneUp, and in the Schedule Post dropdown, choose “Auto-post from RSS feeds”.
Paste in the RSS feed URL that you had copied, then choose the category and which account(s) you would like to auto-post to.
Choose your Call-To-Action button and add your button URL.
Now whenever you post something on Facebook, you can have it automatically published on Google My Business posts, with Call-To-Action buttons on each post.
No Zapier zap required.
Check out OneUp here.