The name Viney is an English surname of Norman origin (France), also a French surname. the name derived from the word "vine", ultimately of Latin origin.
There is of Indian origin, as bearers from India have the surname Viney also. It could be a variant of a more common Indian surname Vinay, the name meaning "modesty".
More can be found here about the name Vinay - http://en.wikipedia.org/wiki/Vinay_(given_name)
and the name Viney - http://www.ancestry.com/name-origin?surname=Viney