Hi @bric ~ Welcome to the Community! 
We don’t have a tally option at this time for either automations or our Formula Column, I’m afraid, so a counter that adds +1 every time a button is pushed won’t be possible at this time.
If it helps, you can see the most recent change was made to an item using The Last Updated Column but for any specific changes and when they were made, you’ll need to check the Item Activity Log .
Otherwise, something you can always try instead would be to use one of our 3rd party platform integrations to build your own automation to count the number of times a specific change has been made in an item:
- How to create an integration using Zapier
- How to create an automation or integration with Integromat
If you are comfortable coding or have access to any developers, you can also build your own app/automation using our API:
If you need additional support on our APIs or apps platform, I would recommend doing a search for your question in our developer community here. You can also post to the community to get help from other monday.com developers.
If you need help building custom integrations, we also have an option for paid assistance through our network of certified monday.com partners. If this interests you, simply fill out this form and someone will be in touch shortly!
I hope this helps! Remember to mark as solved if this answers your question 
Cheers,
Jenna