PPSD has posted the dates for registration for Kindergarten in Providence Public Schools.
This can be found at the following link:
http://www.providenceschools.org/media/159414/registration dates for new kindergarten students.pdf
Note that if you have any interest in sending your child to your neighborhood elementary school, you have the best chance of getting your choice if you enroll your child in Kindergarten at that school. Once the slots are filled by neighborhood students (80%), the remaining slots are given to children from outside the neighborhood (20%)(there may be some exceptions made to this for siblings). If seats reserved for neighborhood children are not filled, they will be given to non-neighborhood students who chose to opt for a non-neighborhood elementary school. After Kindergarten, the only seats available in later grades generally become available through attrition. Hence, it may be much more difficult to enroll your child in your neighborhood elementary school in 1st grade or beyond.