Yellowing leaves on roses is a stress symptom. Unfortunately, many different things could be causing this stress:
Spider mites are common on indoor plants. They are very tiny. Unless you have a bad infestation (at which point you will begin noticing tiny bits of webbing), they are difficult to see with the unaided eye. But hold a piece of white paper under some branches and shake the branches. Spider mites will appear as teeny tiny reddish specks on the paper. They thrive on the dry conditions of air conditioned indoor air.
Over-watering can do it. I wouldn't keep the soil damp all the time. I would water it thoroughly and then not again until the top layer of the soil is drying out. But in the meantime, mist the leaves daily as long as the plant stays indoors. A humidity tray helps too - the plant doesn't like dry indoor air, even without spider mites.
Nutrient deficiencies can be the stress, but so also can fertilizer burn. How have you been feeding it?
You said your porch gets "nothing but sun." If it is truly a porch, not a patio, that sounds unlikely. Porches are attached to houses. Therefore, the porch is necessarily shaded by the house at some parts of the day. What direction does your porch face? If it faces west and gets the hot afternoon sun, that is not a good summer location for your rose bush. Any other direction would probably be fine. I would wait for a cooler, overcast day and get your rose out on the porch.
Keep us posted on how it is doing and what you find!