Open all doors and windows. Put on a paint respirator, rubber gloves and eye goggles. Dip a painter's rag into xylene and wipe the laminate surface to clean all grease, dirt and grime.
Sand the laminate surface with a 120-grit sanding block until the laminate appears dulled. Noticeable hairline scratches will appear, but this is OK. The paint will fill them. Wipe away all dust with a tack cloth.
Run pieces of masking tape on surfaces around the laminate that you don't want paint on. These might include cabinets, window sills and countertops.
Lay painter's plastic over the countertop beneath the laminate backsplash and tape it to the counter. Place a paint tray on the counter and pour a few inches of acrylic paint into it.
Dip a mini roller fitted with a 1/4-inch nap roller cover into the paint. Roll it back and forth on the paint tray until the fibers are loaded.
Roll a thin coat of paint from end to end and top to bottom until the laminate surface is painted. Wait 24 hours and then apply a second coat. Wait another 24 hours and apply a third coat. The more coats applied, the more durable the paint finish will be.