Some math: First some battery math. Batteries come in 3 basic flavors for this part of this discussion, plus a few more divided differently later on.
Starting: High current, low capacity (relative to peak current) Need to be around 80% full or more for best life
MARINE/Deep cycle.. Basically starting, you can go a little lower on SOC, perhaps 75% (But please do not quote me on that floor, may be higher)
DEEP CYCLE (Like the GC-2 Golf Car battery) You can go to 50% SOC safely (WOW, over 2x the avabial power!!!! and they cost less too if you go with GC-2)
Then we get into how much does each size store.. But I'l cover that later as well.
On your fridge. You have a wattage. Likely 100-300 watts. This is what it needs to run (note there are options if you don't need a lot of capacity I can get you an all electric RV fridge that draws less than 50 watts and Runs on 12 volts!!!!! Bit pricey, but then so are the Home type as well)
Let's assume 200 watts.. ok, that is 20 amps at 12 volts. So you want to run at least 8-12 hours so figure you need at least 200 amp hours of USABLE POWER, that is two pair of GC-2 six volt golf car batteries in a series/parallel arrangement like this..
-{6v}+-{6v}+12 volt
-{6v}+-{6v}+12 volt
both left - signs are connected together and both 12 volts are as well.
And a 1,000 watt Pure Sine Wave Inverter to power the fridge.
And a converter (Progressive Industries 9280) to recharge overnight at home.
If you recharge with the generator you can make that a 9260 or even a 9245 and only use one pair of GC-2's.
Now the other division on batteries
The GC-2 (most common) is a flooded wet cell, it should be mounted in a well vented to the outside compartment (either mount on a wall, sealed the compartment and install a loovered outside vent you can open and slide the batteries out for maintenance, Under a step or other location outside) and you should also mount that big inverter AS CLOSE AS POSSIBLE.
AGM batteries are a very well regulated (Valve Regulated Lead Acid) low venting and many mount them INSIDE which is NOT recommended for Flooded wet.
Also flooded wet need to be distilled watered ONLY DISTILLED from time to time.
(Took just shy fo 4 years before I had to wate my Deka's)
There are some other battery types but I do NOT recommend. Either very poor for this type of use or VERY EXPENSIVE.
Now.. I mentioned the RV size electric only units.
Both Domethic and Norcold offer or offered a High Effiency (Danfoss class) Refrigerator that drew liek 40 watts on either 120 or 12 volt I have an ENGLE Chest freezer. That is also of this class (36 watts I run it on battery only it cost like 800 bucks when I got it. The unit I have can be either a freezer or Refrigerator. Will see if I can find a link for you I think this might be ideal for your use.
https://www.thecoolerzone.com/engel/This is not a sales site, this is a "Review" site. that tells you more abou them, You will see photos of htem, They are not large, but they work great
Since for a "Coffee Wagon" you do not need but a fairly small amount of refrigerated storage. They should work, I'd guess 2 of 'em.
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times