Like drawer liners but don’t like the cost?

Use a fabric softener sheet in your drawer which will definitely impart a scent.

Use sachet in your drawers. Sachet can be costly but you could take an old handkerchief, fill it potpourri or inexpensive tea bags, then cinch it up with a ribbon or fold it in half, and sew the open sides.

Spray cologne onto cotton balls and put them in your drawer if you want some scent in your clothes.

Just be careful with this method, because it could stain your clothes, also if you choose to use potpourri that is dyed.

Old scraps of your favorite soap can also provide a light fragrance to a drawer. Make sure the soap is dry and you can put the pieces in a piece of tulle or an old handkerchief.

Scented perfume ads can also be used to give your drawer a nice fragrance. Just make sure that you like the fragrance before you try it. If not, you could always use the perfume ads in your bathroom garbage can to brighten up the smell of your bathroom.

If you actually want to line your drawers, you could use wrapping paper. The wrapping paper may not be scented, but you will have something pretty to line your drawers. For scent just add your own. If you want to line any drawer with an unscented paper, wrapping paper or any other heavy weight unscented paper is the way to go.