I've had some luck with this.  For the past couple years one of the math adjuncts spent his office hours in the learning center.  He was extremely popular and did a land-office business in our drop-in learning center.  (I say"was" because he retired this year."  I suspect math teachers have less paperwork to deal with, so they are a better bet than, for instance, composition teachers.

One of the computer teachers has volunteered to give me a few hours next semester.  She'll be able to help basic writers, too.

At our small institution, instructors just post their office hours on the doors to their offices and on their syllabi.  If they're in the learning center, they just post a note to that effect on their doors.  There's no administrative permission required, or anything.

This might be unhandy on a large campus where the instructor's office and the learning center are half-a-mile apart, but it works on our small campus.