Anyone Have A New Idea To Keep Moisture Out Of Home Safe

If it is only a slight problem put a small bowl of kitty litter in there. ( Make sure it is new not used)
It's cheap and effective, also works pretty well to get the stink out of a fridge that has been turned off for a while

Note the poster said a safe, not a gun safe. Normal safes do not have a place where an air conditioner could be added without some major cutting to make a hole for that product.
And as I mentioned any gel packs, kitty litter, etc is only as good as the maintenence. If you forget to do something with it, over time it could make things worse.
If your safe is in a high humidity area, every time you open the door, all the dehumidfied air comes out and is raplaced with new, nicely full of moistured air again.
And remember that even if you had an A/C unit that could be mouted to the safe, you just have a location for the water removed to drain.
Not sure if still around but a company called Hoffman used to make A/C units mounted on a cabinet. The cabinets were made air tight but not made for safe type of security.
Almost any bank is Air conditioned so placing most of your valuable coins in their safe deposit box is a start to protect them.
Any coins you have at home in an Album, place in a Zip Lock bag and push out as much air as possible.
Coins in 2x2's could be placed in those 20 slotted plastic sheets for coins and then placed in a 3 ringed binder and that too could be placed in a Zip Lock bag.
Naturally the safest solution is to move to a place like Egypt where the humidity is so low, Mummy's have survived for thousands of years.

The poster did say gun safe in his second post....but, anyhow, another cheap method is rice....it absorbs moisture readily and is cheap to replace.

Rechecking my past Electrical Engineering type of work, I again mention Hoffman Enclosures. They are a company that is probably the largest manufacturer of all types of enclosures. One thing I remembered is for hasardous invironments, they make many types of special enclosures.
AND many must be air conditioned.
If you look into their web site you could come up with a thing called a Hoffman Thermoelectric Dehumidifier, Model H20MIT. The H2OMIT® Thermoelectric Dehumidifier removes moisture from the air within an enclosure, providing an inexpensive yet highly effective way to protect electronic and electrical components from condensation. This item is adjustible to any desired Humidity rating you want.
One small problem is since they are the type of organization that primarily does buiness with hugh companies like CommonWealth Edison, their prices are a bit on the high side. BUT you may want to check that out.