Can you have a good economy, but have a lousy job market?

It is possible to have a reasonably good growth rate of the economy but the increase in the number of jobs could be slow. In fact that is the case in India. Its growth rate from mid-1980s is good (internationally). However there is not enough growth in employment. The reasons may depend on the specific context. The main problem in India is the slow growth or stagnation of the lower-end manufacturing. It is this manufacturing that can create millions of new jobs in formal sector for people who get out of agriculture, and who have only school education.

Yes you can have a good economy and a lousy job market since employment is only a part of what makes an economy.