Actually, I just now noticed you are in LA - my brain is constantly on "build for KS weather conditions" mode, so I was picturing a more substantial building than you probably need for your climate. In our climate we need to keep them cool in summer, warm in winter and our winds are legendary so we have to keep those in consideration as well.
I'm still concerned that on their sides there will be too many openings, and you will end up with snakes and rodents living in your coop. Also, if I am picturing the same cinder blocks you have, they are 16L x 6D x 8H. So....putting them on their sides, you will need more bricks to attain the wall height, than standing them the regular direction. Oh - here's an idea, since you have a much warmer climate than we do - why not make a 3-sided coop? You said your run is secure so that might work.
I googled Liquid Nails and concrete and it does appear they have a product that is used to repair concrete so that's probably the product you planned to use? I'm not familiar with that, but it may be the more expensive route to take. Mortar is pretty easy to use. You mix it up in a bucket, use a trowel to smooth it on, and then add the next layer of bricks. Remove the excess that squeezes out at the join and 24 hours later its set pretty hard.
You might talk to someone at your local Lowes about your options there - they may have additional suggestions, and would certainly know more about what works best in the LA climate.