Deeper Darkness block darkvision assuming the spell lower the ambient light level to dark or darker. It also block all non-magical light sources and magical light sources of equal or lower level (meaning you have to heighten a spell to overcome deeper darkness or specifically cast daylight...and the rules are kind of shaky about that).
Unless your fighters have a source for a 4th level light spell their darkvision doesn't work.
If a creature cannot see the target they cannot charge them, because they cannot locate them. However, whether the target can see the person charging is irrelevant. The animal is effectively blind with regard to what it can do, assuming it doesn't have a way to see in supernatural darkness.
So if the ambient light conditions of your location are not normal or bright light to start with casting deeper darkness results in supernatural darkness which none of your players (or likely their enemies) can see through.
I think OP asks if fighter with darkvision can charge while MOUNTED on the creature without one.
Oh...I misunderstood the question.
Well then no, if it can't see through the darkness it can't charge either.
I think OP asks if fighter with darkvision can charge while MOUNTED on the creature without one.
He did...Claxon answered in a round about way, but the answer is there.
The mount is blinded and therefore can not charge. The fighters in question are also quite possibly blinded from the deeper darkness if they only have regular darkvision. Regardless of whether the rider can see or not, the creature actually moving cannot see, and therefore has its movement hampered and can not charge.
I would allow it, as rider directing the horse, but maybe acrobatics DC 10 to move more than half speed for horse (or whatever it is) with rather bad (but funny) consequences of failure.
Not sure about RAW. Probably it can not.
If you don't have line of sight to the opponent at the start of your turn, you can't charge that opponent.
You don't have line of sight to something you can't see...
I can see houseruling something like disastrous consequences on a failed acrobatics check, sure, for thematic reasons.
Well, with that FAQ that says "rider and mount charges in unison" mount need to fullfill charge conditions too.