I've always pronounced it kind of like 'shh'. So 'shinying'. I don't know if that is right or not, I may have misunderstood the chinese grad student who was trying to teach me. I don't have an ear for chinese, as much as I try.
Although my ear for languages is not the best, a Taiwanese colleague pronouces it kind of half-way between sin-ying and shin-ying. The nursery is called Ching Hua Orchids and is located in Hsinying very close to Tainan. Plants with either Hsinying or Ching Hua in their name come from this nursery.
In-Charm Orchids has a nursery in the same general area also and I hope I can make a visit there some time in the not to distant future.