I would second Steven on the point about it being best to try to define exactly what it is you want this role to be able to do. It's much better and much easier to work from that point rather than to try to "shop" the capabilities and figure out what to allow and not allow.
With that said, I've had similar needs and I'm happy to share what we created on the off-chance it helps you figure out what you want. In my case, I had users who were facilitating courses and these facilitators needed to be able to quickly address common user issues, such as lost passwords, and to be able to log in as the participants to troubleshoot issues or questions. In addition, the facilitator needed to be able to log in to each course being developed by the participants. The facilitator also needed to be able to create new users, course shells for participants, and to organize courses within categories.
To meet this neeed, I duplicated the course creator role and made some modifications to that role.
I actually found this role useful on a small Moodle site I administer for departmental Moodle site at a University too. In that case, I wanted to give a professor the ability to create accounts and troubleshoot issues and it's worked well.
Here's a listing of the permissions I changed after creating the duplicate of the course creator role. I then assigned the role at the system level, though you could assign it at the category level if you wanted to limit access even further.
Upload new users from file: Allow
Create users: Allow
Update user profiles: Allow
Manage categories: Allow
See hidden categories: Allow
Create courses: Allow
Login as other users: Allow
In your case, it sounds like you may want this user to be able to create courses and to be able to edit any courses on the site. The ability to edit would be necessary in helping teachers troubleshoot. If that's the case, I would suggest starting with the teacher role so you have all the course editing capabilities and then add the course creator capabilities and any other more advanced capabilities you would like.
Hope this helps--if you have more questions, let us know.