I use sulfur. Some people mix sulfur and lime but I never do and I get good results. Stay away from those chemical fungicides, they work a little better for the short term. In the end you would be better off replacing the rose, rather than polluting your entire yard.
Ill second what someone else wrote. Make sure the rose is planted properly, in good soil, at the proper height. Proper pruning is very important as well. Chances are if the entire plant is already infested with black spot you are going to lose the plant or just tolerate the black spot until it dies. I've seen roses live for years with black spot. The main thing to remember is it is contagious, so if you are growing only one rose it isn't so bad. If you have fifty roses, get rid of the infected plant.

Blackspot spores live on the soil and will splash up onto the plants with the rain. I treat the soil around my plants with ordinary corn meal. Monthly would be best but I do it when I remember.

Clip off any affected leaves. They will never be normal again and all they can do is spread the disease.

Best way to organically deal with a blackspot-susceptible rose? Shovel prune. Even organic fungicides can be problematic and cultural practices alone (e.g. adequate water and soil) won't fix a rose that's just a good old blackspot magnet.

Seriously, if blackspot is particularly virulent on this rose you need to get rid of it and plant a blackspot resistent variety in its place. Goodness knows there are many better choices.

Besides building good soil and practicing IPM, one of the foundations of organic gardening is avoiding plants that have particular pest or disease problems. Make better plant choices.

Well, let me be a little more specific, I would like to remove it, plant a disease resistant rose somewhere else, but I'm renting the house and property. I'm most concerned, can it spread to other flowers or plants nearby? If that's the case I'll beg my landlady to let me remove it. She isn't organic at all, and lives next door.

Don't worry about it then. Not a problem except perhaps for other roses.

Black Spot of roses is specific to roses, it will not spread to other plant species.

Even organic fungicides can be problematic
I'm not sure what marymd meant by that but rather than leaving that blanket statement on the table, I'd like to get more specific. The sulfur, sulfate, and baking soda organic treatments for fungus are all non selective. In that sense they have issues. Corn meal and milk seem to be more of a microbe food and are not a problem that I'm aware of. Shampoo is something I know much less about. It has only recently popped up on the horizon as a 'fungicide.'

Any soap, including shampoos, are bactericides and fungicides, they kill bacteria and fungi. Keep in mind that the FDA came out a few years back and stated that the antibacterial and antimicrobial soaps are no more effective than any other soap, but do have one major problem and that is that they can continue killing the bacteria and fungi in our waste stream, and they expose bacteria and fungi to low doses of these stats which can allow the disease pathogens to develop immunities to them which means we will need more powerful antibacterials then we now know how to make.
Our wastewater people here tell me that because of the use of these antibacterial soaps they must add bacteria to the digestion ponds today.

The shampoo I'm talking about is a mild detergent. It is more of a surfactant to rinse dirt/germs away than an antiseptic like alcohol, iodine, or hydrogen peroxide. I don't think soap or detergent is necessarily antibacterial or antifungal. If they were then we wouldn't need the real antibacterials.

The reason washing your hands cleans the germs off is that there are not many germs that can handle both hot water and the relatively germ free drying from a clean towel, hot air, or a clean paper towel. Soap adds the complexity of a change in pH for the germs to handle in addition to the heat, moisture, and dryness. Somewhere in there might be a clue as to how soap might help stop fungal disease in plants (if it does).

The soaps my grandparents made by reacting wood ash, lye, with animal fats was, and still is a very good bacteria stat. Even many of the detergents used today, without the antibiotics, are effective bacteria stats and is why the FDA, finally, stated that antibacterial soaps are no more effective than any other soap at killing disease pathogens.