1. Speak and teach a second language.
Teachers who speak French, Spanish and Mandarin are much in demand in any school. Add a degree and certifications in those subjects to your credentials and you will be a 'hot' property! Unlike public schools where language skills are necessary just to deal with a non-English speaking population, private schools offer academic courses in French, Spanish
and Mandarin language and literature. Many of these courses lead to AP level examinations. You will have the opportunity to use that honors degree work in foreign languages to your advantage.
2. Hold specialist certifications.
An ESL certificate or a reading specialist certificate will virtually guarantee you employment for life at many schools. Schools which enrol non-English speaking students frequently require those students to master English at a very high level in order to complete their academic course work with good grades. An ESL certified teacher is an integral part of the teaching strategy and an important element in a diverse community. A reading specialist can effectively remediate reading and comprehension skills allowing the language arts teachers to focus on coursework.
3. Be an AP exam reader.
A little prestige never hurts. If you are or have been an AP reader in Art History, Chinese Language and Culture, Environmental Science, European History, Government and Politics, Human Geography, Japanese Language and Culture, Music Theory, Spanish Language, Spanish Literature and World History, for example, you will be in demand.
4. Be willing to relocate.
Not always easy to do, but if you can accept an appointment which requires relocation, your marketability will improve significantly.
5. Offer subjects which are in demand.
This will vary from region to region. But it stands to reason that math and physics teachers will probably be in shorter supply compared with physical education teachers. If you can teach to AP level or have IB teaching experience in your subject, that will increase your marketability too.
Be shrewd. Find a niche. Then work it for all you are worth. Good luck!