A thought on how to get more project fabric.
I'm a quilter, and quilters joke that half of our hobby is making quilts, and the other half is collecting fabric. While most of us have fabric for intended projects, we almost all have either fabric leftover from a project or fabric we bought and are never going to use for some reason. I would suggest going to your local quilt fabric shop and ask if they have a bulletin board. Explain you volunteer teaching sewing at the community center and are looking for fabric donations. A flyer with an easy way for local quilters to donate extra fabric is likely to get results, as often quilters are just looking for a good reason to rehome some fabric. Quilt cottons are great for a lot of projects, including heat safe items (just no metallic fabrics on those) and little pouches.
Youtube and a lot of websites have free patterns that I think would teach sewing skills and create things your students would like. Oven mitts, hot pads (these are a great way to teach quilt piecing, as a simple star block on top of a hot pad looks fancy!), jumbo trivets (I make these for family, huge hot pads that allow a 9x13" glass baking dish to fit), bowl cozies, ice cream cozies, holiday ornaments, book pouches, glasses pouches with flannel inside, etc.
Others have suggested charity quilts for trauma survivors. You could do a class where each student makes a quilt block, then you could sew them together. To do a "quick quilt" that requires less quilting and binding, look into the pillowcase method with a fleece back and simple ties. This is a much faster way to finish quilts than the traditional method and may fit your needs better. A fleece throw blanket can be used as the back, and are often affordably priced.
Also, sheets. Quilt cotton is expensive. Depending on where in the world you are, if you need plain cotton, a king size package of sheets may be cheaper.
This is my favorite tutorial for pillow cases, but there are other great ones online.