I remember, it was about 4:00 PM and I got bored with my OR game and I started Wondertrading. I traded of I think a Zigzagoon, and in return, I got a LV 100 Japanese Lucario with a good move set. Now, it's a staple of my competitive team.
In that case, I'd suggest trading on Wednesday nights around 8pm EST. A lot of people livestream then, so people typically send out shinies and BR Pokemon in hopes of getting screen time. It's a perfect opportunity to get good stuff.