The (Australian) Macquarie Dictionary defines dink as
--verb (t) 1. to convey as a second person on a horse, bicycle, or motorcycle.When I was a kid growing up, we lived less than a block away from the local primary (elementary) school so we walked to school. Some kids had bikes and it was fun to be dinked home. Usually, the person being dinked would ride behind the cyclist on the rack, or sitting over the front handle bars with legs hanging over the front. If the person being dinked was really lucky, the cyclist would ride over the front bar and give their 'passenger' the seat.
--noun 2. a ride obtained from being dinked.
Nobody dinks these days and children today have no idea what the word means. In fact, the word is so particular to certain parts of Australia, that a lot of older people have never heard of it.
Photographer Heidi Swift took this photo of cyclist Chris Horner dinking Billy Demong during the Cascade Cycling Classic in 2008 (from Velo News - which did not use the word dink at all).