The first time I found all 4 Magic Plants, I was just breeding randomly and not keeping track of what I was doing. It took me about 3 weeks to get them all, and I had the game on fast and made new plants as soon as the seeds I had planted were mature. So, it is possible to discover the Magic Plants by sheer luck. Since then, I have found that keeping track of foliage type and flower type on simple spreadsheets produces more predictable results, and I don't wind up breeding the same plants over and over.
One way to inject some new "genes" into your breeding is to buy a seed and breed it with plants you already have. That might get you on the road to new discoveries!