If you're okay painting on a flat surface, all you need is a protective layer impervious to paint. It won't be paper.
Clear vinyl: https://www.joann.com/12-gauge-vinyl-54in-clear/1151489.html can be cut to fit the desk top or allowed to drape over it, even be pinned or tacked to the wall.
Or you could spend even less and buy a plastic tablecloth, the kind that come in colors and are used for birthday parties. Or a durable flannel-backed vinyl tablecloth.
One issue with easels used in a small space is that the work is more likely to be bumped, the easel knocked over, etc. My sister was a teen painter whose greatest work was ruined when she bumped her desk and the easel tottered, then fell--and her painting landed face down.
For that reason, you might consider a book stand rather than an easel. They're more able to stay upright.