N.S.
My husband and I lived there years ago, and we have taken our daughter to MBA each time we vist - big owie on the admission cost, but worth it if your kids love sea life!!! If you are staying overnight in Monterey, you can probably get discount tickets through your hotel. If not, I agree with the other mom below - contact the office and they might be able to direct you to a discount. I think AAA might give a small discount too, if you are a member. One page I read says that craigs list and ebay have tickets for sale - but not sure how reliable those are! Do you have access to an Entertainment book - those offer lots of BOGO admissions to different places
I googled the name of the aquarium plus the word discount and found a coupon page that might be helpful to you for this or other places (below) - and that was just the beginning - you might want to try too - I know I found a few pages like this last time we visited. You can also try just a city name and the word coupon or discount (I'd try both, one at a time- probably bring up different things...) Good luck!!! :-)
http://www.visitcalifornia.com/Fun-Spots/#centralcoast
If you live near enough to go a few times a year, consider a membership - higer upfront cost but it will probably save you big bucks!