Keep in mind that there is no “official” or “correct” way to pray the Rosary. The Rosary is just a devotion, and if someone prays it, he should do so in the way that is most helpful to him.
However, it is recommended that the mysteries contemplated should correspond the liturgical calendar.
For example (as the O.P. asks), it would seem fitting to pray the Joyful Mysteries on Christmas Day, even when Christmas falls on a Friday.
This kind of “change of mysteries” would apply on any solemnity, feast, or memorial that celebrates one of the mysteries in the Rosary.
For example, one would normally pray the Joyful Mysteries on the following days:
- The Solemnity of the Annunciation, celebrated ordinarily on March 25.
- Christmas Day (which is a solemnity, as mentioned above).
- The Feast of the Visitation, celebrated on May 31.
- The Feast of the Presentation, celebrated on February 2.
The Sorrowful Mysteries, on the following days:
- Palm Sunday.
- Good Friday.
- Holy Saturday. (Many people also elect to pray the Sorrowful Mysteries during all of Holy Week.)
- The Feast of the Exaltation of the Holy Cross, celebrated on September 14.
The Glorious Mysteries (those that do not already coincide with a Sunday):
- The Solemnity of the Ascension, even where it is celebrated on a Thursday.
- The Solemnity of the Assumption, celebrated on August 15.
- The Memorial of the Queenship of Mary, celebrated on August 22.
For those who follow the recommendations of John Paul II's Rosarium Virginis Mariae, which recommends praying the so-called Luminous Mysteries on Thursdays and the Joyful Mysteries on Saturdays, the Luminous Mysteries would be prayed on the following days (when they do not already correspond to Thursday):
- The Feast of the Baptism of the Lord, the Sunday after the Epiphany.
- The Feast of the Transfiguration, celebrated on August 6.
- Possibly the Solemnity of Corpus Christi, even when it is celebrated on a Sunday. (Corpus Christi is traditionally celebrated on the Thursday after Trinity Sunday; in most jurisdictions, the solemnity is moved to the nearest Sunday.)