Can you recommend an electric butter cooler?

Rather than something electric or powered, I think an item like these butter keepers will do what you want:

https://www.thespruceeats.com/best-butter-keepers-crocks-5180289

There is available for sale a butter boat with a holder under it where you add some ice & you can still leave your butter on the counter. Sometimes the ice lasts for a good length of time…other times you need to replace the ice frequently. I would think that you could take 2 compatible bowls & put the ice in the bottom bowl & putting the butter in the other & sit on top of the ice. Or find a bowl that works with the butter dish that you’re currently using. I’ve never seen an electric cooler specifically for butter.

Yeah, a “botervloot” is what you need.
I have a metal, shiny one, from my parents’ wedding gifts.
It works (for especially your preferred scenario).
Something like this

At the fast food joint where I worked they melted the butter at room temperature in a stainless steel container, and used a clean painters brush to apply the butter to toast.

You can also put the butter in a squeeze container.

I’ve never even heard of an electric butter cooler!

I already have one of those ceramic butter dishes. The butter still melts. That is why I am seeking an electric one.

Well, Googling it there are several electric butter keepers. I can’t say I’ve ever heard of anyone using one but they’re probably fine. For the ceramic one you have, does it have a layer where you put ice or cold water in it like the ones in the link I posted? A regular ceramic dish won’t cut it.

FYI – what I do is get up and stumble downstairs and take the butter out of the fridge, slice a few pats to soften and go back to bed for a bit. Butter is perfect when I make my toast.

https://www.hammacher.com/product/cordless-temperature-controlled-butter-dish

My guess is that this thing would never look clean. I keep my butter in the fridge.

You might try a butter bell too.

Just place the butter in a small cooler in the morning when it and everything else is cool.

@SnipSnip That looks pretty cool!

@SnipSnip Those were the links I provided in my first post.

Any kind of a butter cooler would require a electric compressor, thermostatic expansion valve, receiver-drier, evaporator coils and condenser coils, tubing, refrigerant, and, of course, an insulated box to house all this refrigeration stuff to keep the butter cool in or at least at room temperature…
How complex do you want this to be??
Get a small refrigerator for your butter and set it at room temperature, if you can. That will fix your butter.

A solid state, thermoelectric cooler would do the job in a small package and at relatively low wattage. Laird TEC. I’d try something in the 10 watt range to start.
Use their Thermal Wizard (on the left side of the page) to calculate the size you need.

I love this question!
Here are some potential sources of Peltier devices.
DigiKey
TETechnology

I picture an aluminum box about the size of the butter. The Peltier device would be mounted with heat conductive adhesive to the middle of the aluminum. The air, waste heat, side of the device would be attached to an inexpensive air heat sink. Power would be supplied by a 5V DC USB charging device you have in your drawer someplace that supplies about ½ to 2 amps. That is 2.5 – 10 watts of power. Plenty.
Use the design apps the websites. You will learn a lot.