I had a childhood friend with this name and the pronunciation listed is not how she and her family pronounced her name. It was less sounding like "Chinese" and more like SHAN-eese (like the English pronunciation of Rhys). Edit: Upon reflection, this may have been because she was a white British girl from a white British family while the name is listed as African-American.
Honestly, The name Shanice is a beautiful name and people need to learn how to pronounce it. Instead, they say "Chinese" and it gets annoying, like for real.