There may be several possibilities for you to obtain a Swiss residence permit under your circumstances:
1) Permit for a common law partner (Konkubinat):
In neighboring Canton Aargau it is possible to obtain a residence permit to live with your common law partner if your relationship is similar to being married, long-standing and this can be so demonstrated. Use Google Translate to translate this web page:
https://www.ag.ch/de/dvi/migration_i...=172044#172044
- If Canton Zurich doesn't have such a permit, you could always live in Aargau near the border to Canton Zurich.
2) Claim to EU/ EFTA citizenship by descent:
If you have not already done so, you could explore whether you have claim to EU/ EFTA citizenship by descent. Some of the better known ones include Irish, Italian and Polish citizenship but there are other EU citizenships that you could possibly be eligible for. This website has a list *:
http://www.whitenewsnow.com/lounge-w...ent-print.html
3) Independent Work Abroad in Switzerland for Recent College Graduates - US Citizens:
Review whether you might be eligible for this program:
http://www.culturalvistas.org/progra...in-switzerland
- As a teacher, I would think that you would want to apply at the international schools, starting in Zurich area and going outwards from there, e.g., you could commute from Zurich to Zug, Bern, Basel, etc. via train.
- You might be able to apply for teaching jobs outside of this Independent Work Abroad program as well.
Also, this website has a list of job boards that might help you to find a job in Switzerland:
http://aso.ch/en/consultation/back-t...-to-find-a-job
Added:
* - I'm not normally a reader of the "White News Now" website but the blogger has developed a fairly comprehensive list of European citizenship by descent.