There is a reason that I answered the way I did…stemming from my experiences with the Religious Communities. in the United States
The inquirer is not asking about Communities that promote the Rosary or have a historical connection to the Rosary – he is seeking a Community that prays the Rosary in common, as community. That is a very specific question. One can, therefore, immediately exclude the classical monastic orders, for example.
This is what the Southern Province of Dominicans says about the daily life of a friar:
A typical day in the novitiate begins with Lauds (Morning Prayer) followed by the community Mass where the friars are often joined by students, faculty and staff from the University of Dallas as well as others from the local neighborhood. After breakfast, the novices are frequently engaged in common study with the novice master or a scholar brought in as the opportunity and need arise.
Time during the day is also allotted for private prayer and study. Each novice shares in the duties of caring for the house and also chooses a specific form of apostolic ministry to round out the balance of prayer, study, and ministry. The novices are encouraged to develop their own creative gifts in areas of personal enrichment and to regularly exercise. Vespers (Evening Prayer) is celebrated at 5 PM followed by recreation and dinner. The day concludes with Compline (Night Prayer) at 7:45pm.
In contrast, the rosary is prayed as a community daily at 4:30 by the Norbertine Abbey I mentioned – see here
And the rosary is prayed as a community three days per week by the Conventual Franciscans of Marytown – see here.
From experience, I know that there are Carmelite hermits who do pray the Rosary as a community but this is atypical for Carmelite friars
The last priory of Brigittine Monks, however, do so
If the recitation of the Rosary as a community is an important or essential value to this inquirer about Religious life, then that is a criteria he should place at the top of his list since it is not frequently encountered in male Religious life, as a community exercise.
If the inquirer were a woman, I could offer a number of American communities to pursue.