Quick advice, you should always travel with these: https://www.amazon.com/Emergency-Poncho-Weather-Protection-Zone%C2%AE/dp/B000Y9IUXG?ie=UTF8&*Version*=1&*entries*=0
First of all, where in Italy ? I think it might be unusual for rain in the entire country for an entire week all day and night long. . Secondly, weather forecasts arent always accurate, especially a week out. We were in Italy for almost 3 weeks in May - Milan, Florence, Venice, Rome, Sorrento and points in between.
Often the forecast called for rain, but it never rained. Or when it rained in the morning, or night - it didn't last very long and it was never torrential. We tend to travel light, so we just bought ponchos that easily fold up, or can even be tossed out. You can pick these up before you travel. You might also want to consider getting a pair of crocs, you can wear them rain or shine.
We didn't bring an umbrella, but you can always take a compact one - or you can get one there if you need it.
Lastly, just have a "rain" plan. Museum or other indoor location, or use the rain as an excuse to go shopping.