I fixed this problem by uninstalling the Dialogflow agent associated with the project:
- Go to https://console.dialogflow.com
- Click on the settings item in the upper left corner (cog icon next to the agent name)
- Confirm that this agent is in the project you are trying to delete. If not, select the agent that is in the project.
- Click "Delete this agent" at the bottom of the page and follow the instructions to remove the agent
- Try deleting the project again.