I Want To Make Banana Bread And My Bananas Aren't Brown. Can I Still Make It?

You sure can, make sure they are ripe enough to be able to mush them all up.  but you do not have to have brown bananas to make the bread. Have fun and save me some  ha ha

I mash them up on a dinner plate, put a piece of plastic wrap over them, and let them sit for a bit while I get all the other ingredients for the bread together.  You can also mash in a tablespoon of applesauce with them to get them a bit mushier (and it won't affect the taste at all!). 
I also add a half cup of drained crushed pineapple, or a 1/4 cup chopped maraschino cherries, or a 1/3 cup grated white or milk chocolate, or a 1/2 cup mini chocolate chips to the bread for variety.  My kids loved it marbled at times  -- take a cup of the batter and mix it with baker's cocoa, then blop it on top of the batter in the pan and lightly swirl it into the batter.
Hope your bread came out well when you made it!
Moe

To brown them faster I reccommend freezing them, then thawing them, but thaw them on the counter. They don't have to be completely frozen for this to work, just put them in th freezer for 1-11/2 hours then take them out and let them get back to room temp.

Yes, they'll change color with the heat and ingredients

you may boil the banana first then go on with the rest....

I am sure that you know that the reason for ripe bananas is the more ripe the more flavor. Yea one reason is to make them softer to mash but you can always use a food blender if need be. Also try adding some banana flavor if they are not to ripe and maybe add some yellow food coloring. I have tried it this way an my kids love it!

Bananas need to be over ripe for banana bread, they need to be very soft so you can mash them.