According to
this guide by Aeter, you only have to water the black rose once with a golden watering can for it to have a 50% chance of spawning a gold rose the next time it breeds or clones, even if you only water it with a regular can or rain on future days. However, once it breeds or clones any color rose, you have to water it with the golden can again for another chance at a gold rose. So you do need the golden watering can, but you only need to use it once and not every day. Also, the guide helpfully points out that you can conserve your golden watering can durability by watering the ground with a regular watering can first and then coming in with the golden watering can afterward since the golden can won't lose any durability if all of the tiles it waters have already been watered on the same day.