Quizzie I feel your pain. I don't have an entire black stove but have a stainless steel one but the controls are in black and plated on a little shiny black plate. I am anal and here is the only way I get it cleaned to my satisfaction.
Spray my stove (steel and black parts) with greased lightening (love the product). I leave it on the stove for 10 minutes. I then clean it with a damp sponge. Next I take a dry microfiber cloth and dry the stove until it shines. Yes the black part shines like it's brand new.
Just keep in mind that any appliances - black, white, stainless need to be cleaned after every use to keep them in good condition. I am deligent at cleaning after every cooking chore and then once a week I recruit my husband to do detail cleaning (using elbow grease). As I stated earlier I am extremely anal about a clean and shiny kitchen
although I know the minute my kids eat or the minute I cook (which I do almost every day) it will be back to it's original state and I will have to clean all over again.