Is your wife working here on a Japanese work visa or on the US military base? If she has a Japanese work visa, she could apply for a dependant visa for you. This wouldn't give you the right to work immediately. You'd have to apply for special permission to do so at the local immigration office.
Sure, this isn't the best time to be looking for an English teaching job in Japan, but it isn't all that bad. There are noticeably fewer full-time jobs that pay well, but there are still plenty of part-time ones around.