First, trash Bonk as a mascot for the thing. I love Bonk, but come on. A baby caveman with a giant head isn't going to sell consoles. Instead, make Bomberman your mascot, because seriously, who hasn't heard of Bomberman?
Second, get some decent exclusives. Scrolling shooters are nice and all, but if you want to make it big, outside of Japan, you need to appeal to Americans. Get some more platformers on there! Heck, get some more JRPGS while you're at it!
It might be a good idea to make a deal with Square and/or Enix to get some of their games over to the system. They don't even have to be exclusives. If people have another way to play Final Fantasy, then that's all the better.
I wouldn't know who to contact about getting a decent platformer on there. That might need to be done in-house. I think Bonk is a good game, but let's face it, Bonk doesn't exactly have "attitude", and his games don't even have the depth of something like Super Mario Bros 3.
Third, advertise!
You don't have to go mad, but you need people to at least hear about your console. Also, see about smearing the competition. You don't even have to tell the truth for that part.
Forth, redesign the console to look as edgy as possible. (It'll go well with the advertising.)
I'm thinking more angles! More lines! I want it to practically have spikes! What we have isn't too bad, but it could definitely be better.
Also build the multi-tap directly into the system. Only being able to plug one controller in without a peripheral is a huge turnoff for most customers.
Lastly, give it a pack-in game. Preferably Bomberman. It's a decent enough game, plenty of replay value, and parents will be obligated to buy a second controller for the multiplayer. Not only that, but name any parent who isn't tempted to buy the cheap console that comes with a free game, over the expensive console that requires you to buy a game separately just to use the darn thing.
Do all that, and people will be singing the console praises for decades. The next step will be figuring out how to successfully transition to the console generation afterwards, but I'm obviously getting ahead of myself. (Although to do that, just ensure it's a cheap console that uses CDs and is really good at doing 3D graphics.)