Ugly, brown stains are a common feature of mobile home ceilings. They develop when roof leaks or condensation causes water to drip onto the ceiling tiles from above.

They persist because removal is not as simple as painting over the stain. The stain “bleeds” through paint leaving it as ugly as before. In addition, many mobile home ceilings are made with a sprayed-on acoustical texture which is VERY fragile. Painting it with a roller or brushing on heavy latex paint is a good way to pull off some of the texture, leaving a bare, untextured area. Fortunately, stains are easy to cover if you have the right materials.
While you are shopping you may also want to buy some of the blue masking tapes. It costs more than standard masking tape, but comes off when you are done, without leaving adhesive behind or pulling anything off when it peels away.
Mobile Home Repair - Ceiling Stains
At home, mask the area you plan to spray and put an old sheet or something on the floor. Then follow the directions on the can to do the actual spraying. Two light coats with adequate drying time between them are better than one heavy coat.

In most cases, the color of the new area will be close enough to the old that no additional topcoat is needed. The fact is, people seldom look up. With the really obvious stain gone, there will be nothing to draw the eye to what is probably a very subtle difference in color.
The repair described here will cover water stains on ceiling tiles or wallboard anywhere, not just in mobile homes.