We give some alternatives, plus full instructions on growing sprouts, below...
We've read instructions that suggest clean panty hose. If you have a pair with a run in them, reuse them! They would work well on an alfalfa jar (or to hold decorated Huevos Haminados while they boil).
Essentially, you need a breathable top that allows you to pour out water after rinsing the seeds, without pouring out the seeds. Other than that, the seeds sprout and grow in the jar, not attached to the cheese cloth. So we suspect you could also hold a small, fine mesh strainer on top of the jar while you pour out the water, then just tap the seeds that stick to it back into the jar. Leave the jar open or cover it with a light cloth.
Here are the full instructions:
Any other ideas from alfalfa growers out there?