Is it possible to recharge a dehumidifier
TLDR: Not just no, but heck no. 

Throwing good money after very bad

First, electricity costs: any dehumidifier old enough to use R-22 is also super inefficient as-built: The government's Energy Star program has really pushed/incentivized manufacturers to make appliances more efficient, and wow, have they ever done it!  We constantly have people asking how to connect a 15-20A whole-house air conditioning unit to the old 30A wiring that their obsolete unit required.  You will literally save the cost of the new unit in a few years of use, even if you didn't also have to fix it.  

But you also have to fix it.  Here's the thing.  Geordi LaForge didn't "beam" the R-22 out of your unit... it leaked out via a leak you're not even thinking about yet.   The leak is quite likely due to general deterioration of the unit, e.g. corrosion on the aluminum evaporator between the fins, and you will find the unit entirely unfixable in any practical sense. Yes, you can fix the one leak, but right next to it are 8 more places leaks about to occur.  

You would have to retrofit a Schrader valve, charge the unit with R-22 and dye markers to even find the leak, so we're talking at least 2 charges of R-22 if you can quickly fix it, and most likely you can't.  Do you have experience fixing refrigerant leaks? Now it's even more R-22 as you learn.  And if you botch the repair in a way that finally kills the unit... then it's all wasted. 

Realistically the best you could even hope for is one more season of service. Is that worth the expense, R-22 and risk? Of course it isn't. 

I'm a big fan of the thrifty gene, reuse-ability and avoiding the throwaway economy, but there are limits, for Pete's sake!  Obsolescence/efficiency matter. 

You cannot legally service this yourself

Because the law restricts freon sales (the existence of a black market does not mean it is legal), and you need licensure, not least because you must (be competent and equipped to) recover any recoverable freon, e.g. the stuff suspended in the oil.  

Here's what they don't want (for below reasons):  Cleetus  refills unit.  Cleetus did not understand that missing freon means you have a leak.  Cleetus assumes botched refill, refills again.  That leaks out too.  Cleetus finally gets a clue and adds some dye marker (third refill now), finds leak at freshly installed Shrader valve.  Fixes that.  Refills again.  Finds real leak, makes amateur-hour attempt to fix.  Refills again.  You're getting the picture. The government cares because of the freon, but it's bad for Cleetus too: cumulatively, Cleetus has spent more in cash than buying a brand-new one, not to mention about $1000 worth of Cleetus' time. 

The government doesn't allow that, which is why you need to either get the training, licensure, and equipment... or leave it to the pros. 

Note that this article is from 2010.

Substitutes available. Asterisk.

The refrigeration cycle works on the principle of the gas laws.  Almost any liquid or gas will work as a refrigerant as long as its vapor temperature and vapor pressure are in a practical range, and the equipment is tuned for that range.  It's also helpful if the refrigerant isn't corrosive, poisonous or flammable, though that last one is negotiable :)   So there are lots of choices. 

However, every one will have its tricks and traps. For instance some very good refrigerants are incompatible with the mineral oil used in R-22 units (and they have a solution for that). 

Why

R-22 is basically the architectural version of R-12.  And if you followed what happened in the 70s/80s with the R-12 phaseout, that has also been happening with R-22.  

Nothing about refrigerant requires freon per se - the refrigerant cycle will work with any gas, but the equipment needs to be tuned for a particular boiling point and vapor pressure. But many are corrosive, toxic, flammable etc. (R290 actually is propane, and foam cups have been blown with pentane since the 50s). 

These are extremely simple molecules - a carbon with some fluorines and chlorines tacked on. Atomically, those two bond quite violently, making the molecule rather stable after it is created. That was the idea; have a molecule so tightly bound it won't react with anything, and thus, is non-toxic.  Much like a noble gas (helium, argon, xenon etc.) but that boils at a useful temperature and pressure for air conditioning.  The scientists really patted themselves on the back with these. 

The molecules were presumed to be so stable that they couldn't interact with anything. Nobody imagined what would happen in the high atmosphere.  Turns out under those extreme conditions, they do react, and they were tearing part of the atmosphere off the planet. Even worse, the reaction finished with the freon intact, and the destruction would repeat again, and again, and again.  (this is called being a "catalyst"). 

Rather than go underground and make Kate Beckinsdale our queen, the world decided (in Montreal) it was less destructive to the economy to just phase out those refrigerants and blowing agents.  And it's working... but not fast enough; I'm almost out of sunscreen!

I don't know if you were around for the R-12 phase-out, but they pulled that lickety-split (considering they had to retool a whole supply chain).  R-12 went first becuase it was the most damaging, it went in vehicles which ran in hostile high-vibration environments so they had a lot of leaks, were often wrecked and scrapped, etc. R-22 was also a problem but not as urgent, since residential systems last a lot longer. 

Anyway, they did phase out R-22, starting by putting pressure on equipment manufacturers to change to safe refrigerants. They slowed production; for the last 10 years they've only made 10% of the R-22 they used to, and that did drive up prices, but it also reduced demand, since homeowners with older systems were driven into new systems both by freon costs and by efficiency gains, which paid for the conversion in electricity savings!  Around here we see lots of people installing A/C systems needing 15A and 20A breakers - on old wiring with 30A breakers.  Sign of the times!

Production has been suppressed for a decade, but very recently, in Jan 1 2020, production was banned altogether.  All R-22 on the market is either 


new old stock
Recycled freon (since servicers are required to "vampire out" remaining freon and send it up the recycling chain to be reused or annihilated, that's part of why you need licensure to handle freon). 
Black market stuff from the third world, but in that case more likely: 
Fake
A "substitute", that could be viable if the installer knew what it was and how to navigate its tricks and traps (but they aren't saying, and you're proceeding assuming it's real R-22). *


Since the ban, you can expect prices to be a "hockey stick" graph as old/recoverable stock is used up. Since it was only banned Jan 1, we're just rounding the corner, and prices will go ballistic from here. 





* There's lots of R-12A on the market; read the fine print, it's not even slightly R-12.