Romahappydays.com manage now 20 apartments in Vatican and Trastevere area for short and long term stay. Price for days start from 60 euro all inclusive for two persons; 400 euro/week all inclusive for two persons and 1000 euro/month all inclusive for two persons.
Please visit our site to get more info and book by PAYPAL.
www.romahappydays.com/dblog

In google I have also found those sites:

Rome Apartments
Rome Vacation Rentals

And if you want to compare all Rome hotels, you can take a look at this free hotel reservation comparison website, that lists all Rome hotels, from cheap to top class.