Sounds like a fungus. Remove infected leaves and branches and trash them also rake up any leaves that dropped. When you water only water low to the ground do not spray the rose from the hose that's how the fungus spreads. Roses like morning sun and 6 to 8 hours of sunlight will keep the healthy. They also need good air circulation, good organic soil that drains well, well rotted compose and prune regular.
Spray with a funguscide every 7 to 14 days even if you don't see a fungus this will prevent a fungus. Please do not compost the infected leaves. Wash all tools used with warm soapy water and wipe down with alcohol.