Here are the ones I know of anyways:
1. Our Lady of Victories, Woonsocket - I played in this now-closed church for a very short time early in my career. It's the first Casavant I had ever encountered. This one was a tracker built in 1896, two manuals, roughly 17 ranks. Last I had heard, this organ was being restored for the Saint Ann's Culture Center (formerly St. Ann's Church, also closed).
2. Saint Matthew, Central Falls - This IV/70 beast is an interesting one. The build date, I believe, is 1925, built under the "Audsley System", named after George Audsley. The manuals, from bottom to top, go as follows:
There is the "Pedal Organ", and a floating division called the "Aerial Organ". The Aerial Organ is located under some grillwork in the floor up front. Those pipes are Hook and Hastings. In the late 1960's, then-organist Mr. Dupont added a three-manual chancel console (by Austin) so he could play the organ from downstairs. The Austin console was recently replaced by a used Aeolian-Skinner console. The Casavant console upstairs remains, and still plays.
First Organ (Great)
Second Organ (Swell - has two subdivisions, simply named "First Sub Division" and "Second Sub Division")
Third Organ (Choir - also with two similarly named subdivisions, like the Swell)
Fourth Organ (Solo)
3. The Sisters of Mercy Chapel, Cumberland - has a II/12 Casavant built around 1960 that follows Baroque tonal lines.
4. Holy Family, Woonsocket - a working III/39 instrument, the largest pipe organ in Woonsocket.
5. Our Lady of Consolation, Pawtucket - a barely-working III/24 instrument. The parish is not exactly well-to-do financially, so organ repairs, sadly, are not exactly on the priority list there.
6. Grace Church (Episcopal), Providence - this 103-rank monster is on a three-manual console. There are separate divsions for chancel and gallery.
7. Saint Cecilia, Pawtucket - not only is this three-manual instrument of 30-some ranks not functioning, it's replacement organ is a Hammond! Shameful for a parish named after the Patroness of Sacred Music!
8. Cathedral of Saints Peter and Paul, Providence - at IV/128, this 1972 instrument, built under the supervision of then-music director C. Alexander Peloquin, is the largest church organ in Rhode Island, and one of the world's largest trackers! I'm always awed with the visibile expression shutters as they open and close. The 1964-built III/84 electropneumatic Casavant at St. Anne's in Fall River, Massachusetts, has a similar style case. The builders had suggested a four-manual console at St. Anne's. However, since the organist was short, he asked for a three-manual instead.
There may be more Casavants in RI. If there is, please let me know.