I like to breed Pokemon on my commute and then give them away on GTS or GTS Negotations.
Recently I came across a girl from Spain. I offered starters, Zorua and many many Pokemon not obtainable in B/W, but she kept clicking the unhappy face. It didn't seem like she already had most of those, but she just wanted something very specific. Finally, I showed her an Eevee and, yes, that was she wanted. I gave it to her and then disconnected. I am sure she didn't want to come across rude, but pfff...
On your trainer card, you can set the greeting message to something like "Do you want to trade Eevee?", but I guess she didn't know about this, or the "Unown keyboard method".
It would really help if there were an option to just ask for a particular species (also if not yet in your Pokedex).