Proper paint preparation is imperative to success. Remove all the hardware from your roll top desk, such as drawer pulls and knobs. Set them aside and save the screws. If your desk has previously been treated with paint, polyurethane, sealers or wax, use the appropriate stripper according to the manufacturer's instructions to get down to the bare wood. Open the roll top and strip the inside of the desk as well, if necessary.
A slightly rough surface will help the paint better adhere to the surface, which will result in less of a chance that the paint will peel. Sand the roll top with a fine grain damp sanding sponge, which will get into the ridges of the roll top better than a flat palm sanders. Use a palm sander to get the broad, flat areas, such as the sides or the top of the desk. Wipe the desk down with a tack cloth, being sure to get into the ridges of the roll top. Sand the inside of the desk as well.
Open the roll top so there is about 1/2 inch between the roll top and desk top. Lay paper on the desk top to catch any drips. Place a piece of stiff paper or an index card in the space between the edge of the roll top and the side of the desk. The paper will prevent drips of primer from caught in the roll top track. Using side-to-side strokes, brush on a very light coating of primer on the roll top, loading just a little primer on the brush as you go. Move the paper from one side to the other as you get close to the track edges, or swap out the paper for a clean sheet if it gets too much paint on it. If drips get into the roll top creases, blot your brush on a rag and brush over the creases to pick up and smooth out the drips to prevent clumping. Remove the papers, let the roll top dry and open the desk top. Prime the rest of the desk on the sides, top, the desk surface and all parts under the roll top, drawer faces and leg area.
Let the primer dry according to the manufacturer. Drop the roll top again, leaving the 1/2-inch space. Place paper under it and use paper or index cards to paint the roll top the same way you did when you primed it. Paint a very light coat, using side-to-side strokes, on the roll top and let it dry. Open the roll top and paint the rest of the desk. When the desk is dry, close the roll top and re-attach the hardware. Open and close the roll top a couple of times each day to prevent the top from sticking as the paint cures. Leave the roll top ajar for a few days to help the desk to air out.