What should work:

• Create a security role e.g. "Events-editor"
• Add the required user(s) to this role
• Modify the module settings to allow the role "Events-editor" to "Edit module" (second check box column)

Now the user(s) in the role  "Events-editor" should be able to add and edit events and not be able to edit the module settings.

If needed, you can combine this with Event moderation, so that 1 role can add events, and another role has to approve the event before it is published.

This is a bug in DNN 5.1 for all modules -> see here

It should be fixed in DNN 5.11

Normally you should only have the permission to edit the module settings if you are page editor.

Cheers
Renato

I have just created a clean out-of-the-box DNN 4.9.4 site with 1 subportal used for testing. Installed Events module and created the Event structure as I described earlier. Works as I described.

What version of Events and DNN are you working?