Well someone sure lives up to his name...
I know this will be depressing but no. Trades take a long time & 60 pokemon will take a long time to trade because there isn't a faster way. You might want to consider only takeing Pokemon only EV trained & if they all are, only Pokemon at a certain Level & up like 50 or 70 +. If that doesn't work, well only take your top 10 favourites or something. Game freak made it so that trades are slower ing gen IV than any other generation, even 3. You might want to try watching a good tv show while doing this if those 60 Pokemon are that good. It will help pass time because I had 90 Pokemon to trade once so I can feel your pain. NOT FUN.
Hope this helped :)