You may well struggle, as most schools/clubs like people who can pick up the slack on the weekends with trial lessons, especially if you're only working part time.
What you would need to do is find students who want to learn to fly on the days you are available. Otherwise, if they are unable to consistantly put the same students with you, you will not have any work.
It's difficult for anyone to get by on a full time instructor wage, but it's a sacrafice many of us make to do the thing we love. Unfortunately, I don't see instructor wages going up anytime soon, with flying school margins already pretty tight.