it is pretty easy to 'black out' the back. although it is easier prior to putting water into it... (unless you can get access to the back side easily)
Use RUSTOLEUM flat black paint. it comes in a small 1/2 pint container... it is oil based, but it is easy to put on and dries VERY fast.
use a cheap, disposable roller, (weenie roller).. and a plastic or disposable tray. No need to mask off stuff. it is okay to paint the trim. in fact it probably looks better. just roll and jam the roller into the groove of the glass and plastic trim, then roll the trim to get rid of drips or paint build up.
If paint gets on the sides, just let it dry, then when dry, use a razor to scrap it off...
It takes me about 1-2 minutes to apply a coat, then about 15-20 minutes for drying, then apply another coat...
While waiting for the paint to dry, wrap the roller in plastic wrap, or the plastic that the roller came in to keep the air out and to keep the roller from drying...
total cost should be about $10 max