Bill,
The list of available sounds is on the Ring website, but you have to login to the Railpro part of the page to see it. So no, there is no publicly available list. Here's what Ring has, copied directly from the site. This forum is a little more "publicly available" as people should be able to read the posts without having an account.
Alco 539T
Bell Bronze
Bell Challenger
Bell Electric
Bell GE Steel
Bell Howard
Bell Jupiter
Bell NP 765
Bell Steam 1
Bell Steam 2
Boiler Blowdown
Brake Automatic Release
Brake Automatic Set
Break SafeSet Release
Break SafeSet Set
Chicken Sounds
Coupler Clank
Cow Sounds
Diesel Bell
Diesel Engine
Diesel Horn
Duck Sounds
Dynamic Brake
Dynamic Break Dash 8
EMD 567
EMD 645 Roots Blower
EMD 645 Turbo
EMD 645-20
EMD 710
GE 7FDL-16
Gevo
Goat Sounds
GTEL Turbine
Handbrake Release
Handbrake Set
Horn Ahooga
Horn Leslie 3 Chime
Horn Leslie A-200
Horn Leslie S-2M
Horn Nathan 3 Chime
Horn Nathan K-13
Horn Nathan K-3HA-R2
Horn Nathan K5-CA-LS 3Ch
Horn Nathan K5-CA-LS 5Ch
Horn Nathan KS-1L
Horn Nathan KSV-2
Horn Nathan P-124
Horn Prime 920
Horn Wabco E2
Horse Sounds
Nathan K5H-R24 5 Chime
Pig Sounds
Pop Off
Rooster Sounds
Sanding
Sheep Sounds
Shoveling Coal
Start Up Warning
Steam Bell
Steam Heavy
Steam Light
Steam Whistle
Water Fill
Whistle 800 Class
Whistle Baldwin 3 Chime
Whistle Frisco 6 Chime
Whistle Rio Grande 3 Chm
-Kevin