What could a little paint do to hurt a washer and dryer that should be retired anyway?
Go buy some Krylon, or whatever, and follow the label instructions on the can. Be sure to wash the machines really well with TSP (tri sodium phosphate) which is also available at most paint departments WEAR GLOVES!
To mask off the parts you don't want painted -the control panel for instance- use BLUE masking tape and Paint Masking paper. Use a screwdriver to remove those neat little chrome handles and such.
Treat any rust spots with rust remover first, or sand and prime... Use gloves with the rust remover too!
Have fun, remember that NEW washers and dryers don't really cost that much, and you may notice your clothes stay cleaner longer in better shape, the wash doesn't take so long, isn't as loud, etc.