What kind of music job opportunities can a music minor get?

You may have a few options, which will differ depending on whether your minor was in performance or composition and what kind of skills you were trained in. If you minored in performance then teaching and/or playing in a gigging band (a cover band, wedding band, or other event-based group) are options. The type of band that gets the most work will depend on your region (Scottish pipe bands get booked all the time in the Pacific Northwest, Klezmer bands get a lot of work in New York) and it may be worth learning a new style and repertoire to get into the right kind of bands. Any sort of gigging band will generally have an on and an off season, which can help you if you're scheduling around another job but also be a problem if you're relying on that income to pay your bills. Most professional musicians I've known have played in multiple styles to keep their options open. Both teaching and performing allow you to schedule around another job and can be relatively profitable if you manage them well. When you're figuring out how lucrative a paying gig is, make sure to factor in transportation and the upkeep of your equipment, both of which can seriously eat into your take-home.

A composition minor (like I have) isn't as easy to turn into paying work, but it can be done. Teaching and tutoring are still options, especially if your minor came from a competitive program and you can help students get into it. If you have great ears and notation skills then you can find a certain amount of work doing transcription and arranging, though it tends to be sporadic. Some houses of worship pay their music/choir directors, as do some theater companies that stage musical productions. Depending on your area, this may be one of the best-paying and most stable options.

The hardest part of all of these is going to be finding a way to lock in a steady income that you know will cover your loan payments. I recommend taking advantage of any advising you can get through school, your bank, or government programs that will help you manage your debt, and potentially using a tool like Mint or YNAB to help manage your finances.

There are 1000's of jobs. Not all make much money. I warn most of my students that they should pursue music jobs because they can't see themselves doing anything else. If you wanted to make money there are many more obviously profitable job choices.
Read these: http://www.nytimes.com/2015/08/23/magazine/the-creative-apocalypse-that-wasnt.html
https://www.careersinmusic.com/music-occupations/

Careers in Composition
Arranger, producer, orchestrator, composer, film scorer/composer, jingle writer, songwriter, transcriber, copyist, conductor

Careers in Contemporary Writing and Production
Arranger, producer, orchestrator, composer, film scorer/composer, jingle writer, songwriter, transcriber, copyist, conductor

Careers in Electronic Production and Design
MIDI technician, programmer, performing synthesist, music sequencer, sound designer

Careers in Film Scoring
Film composer, music editor, music supervisor/director, film arranger/adapter, film conductor, film music orchestrator, synthesis specialist, theme specialist

Careers in Jazz Composition
Jazz composer, jingle writer, film scorer/composer, arranger/adapter, songwriter, orchestrator, conductor, copyist, educator/teacher, transcriber, editor (print music publishing)

Careers in Music Business/Management
Advertising executive, booking agent, business manager, field merchandiser, music publisher, personal manager, professional manager

Careers in Music Education
Choir director, college/conservatory/university music educator, secondary school music teacher, elementary school music teacher, music supervisor, private instructor

Careers in Music Production and Engineering
MIDI engineer, music director, producer, program director, recording engineer, studio director/manager

Careers in Music Therapy
Music therapist, creative arts therapist, health care delivery professional in hospitals, hospice facilities, substance abuse programs, oncology treatment centers, pain/stress management clinics, correctional facilities, or special education settings

Careers in Performance
Vocal/instrumental soloist, session musician, general business musician, performing artist, orchestra/group member, background vocalist, floor show band member

Careers in Professional Music
Performance careers for vocalists, bassists, brass musicians, guitarists, percussionists, pianists, string players, and woodwind players

Careers in Songwriting
Composer, jingle writer, lyricist, producer/songwriter, performing singer-songwriter, staff or freelance songwriter

Is difficult.
You may get any job to help you.

A minor will not open additional opportunities on its own. In conjunction with a business degree, for example, it could open doors in arts administration. A music minor with a degree in a computer related discipline would potentially open doors for music notation companies, music related app developers, or other opportunities like Spotify or Amazon Music. You do not need a music degree/minor to perform, compose, record, etc. You would need to gain the experience and knowledge through taking lessons, networking, and doing a good job on the gigs you get. Eventually you'll ascend the ranks of contractors and make a little money. As Mr. Cantor stated previously, music does not have a lot of money in it. If you're interested in making money, music is not the right industry.