Recent interest in the Vatican led me to investigate their web site, and I found out a bit about Vatican Radio.
The Vatican broadcasts on five different channels, all of which you can hear via the internet.
On Channel One which is called Vatican Radio “One-O-Five live”, there are Morning prayers in Latin at 6.30 to 7.00 Central European Time, Mass in Latin 7.30 to 8.00, Rosary in Latin 20.40 to 21.00, and Night Prayers in Latin 22.30 to 23.00.
See the daily and Sunday schedule here. It includes programmes in Esperanto!
Channel 2 has Vespers in Latin at 17.00 to 17.30.