Question: I have one copy for my Wii, but now my girlfriend would like to play co-op with me on our Wii U. I dont really want to go out and buy a second copy if we can't play over LAN together now that WiiConnect24 is no longer on service.

Also, please don't recommend buying New Leaf. We already own it but want something we can play on the big screen.

Answer: 
No, ACCF doesn't and has never worked over LAN.

Why not Wiimmfi? It has full support for ACCF.
You can still play Animal Crossing city Folk or lets go to the City using the new WIIMMFI servers. They are private and created to replace the Nintendo WFC servers that closed down.
All you need is a patched copy of ACCF or download the patcher for ACCF from WIIMMFI. You can google to find out all you need.