Probably commemorates Frederick Blackwood, 1st Marquis of Dufferin and Ava, or one of his family. See Ava Street for further details.
The Marquess of Dufferin and Ava was appointed Lord Warden of the Cinque Ports with the official residence as Walmer in Kent - in 1891. A very symbolically important honour within the UK. This prestigious appointment is recognised in the naming of several streets off the Ormeau Road.
Ava Avenue was originally called Ava Street when it developed in 1889 but was later changed to Ava Avenue.
"that on the application of Mr John Russell on behalf of the owners a new street off Ormeau Road opposite Park Road be named Ava Street and a new street off same be named Burmah Street". (14th October 1889).
"That on the application of the owners of property the name of Ava Street, be changed to Ava Avenue and that Mr Wm. Clarke of No.1 Buncrana, Ormeau Road, on their behalf be informed thereof". (Improvement Committee, 4th October 1893).