I have a Carver single speed bike that I want to convert to multi speed. The frame does not have a derailleur hanger, so I'll need to use an internally geared rear hub. I've no experience with such, so I'm wondering if anyone can suggest something.
Thanx!
Nor in Iowa

Lot's of choices of internal hubs, with SA or Taiwan introducing a nice selection of hubs including fixed gear 3-speed. Offhand, I don't know of material quality issues with any so it's a wide open field. One consideration is axle width, look for one that matches your frame or has enough axle length to accept spacers, otherwise you'll need to squeeze your rear triangle down a bit (steel only).

Also, and this is opinion only, simpler hubs seem to work and last better, so try to stick to proven, simple hubs like 3 and 5 speed models, rather than trying to get touring type wide gearing with 11 speeds for example. If you need wide gearing, consider building this bike as a city bike, and buying a touring or mtn bike for those applications.

Sturmey Archer 3 speeds have alternate axles to build up a narrow axle hub .

Brompton uses a 120 wide Hub in their folders..

People have used The Sturmey 8 speed in Bromptons,
taking off and thinning axle spacers , to reduce width

Los of newer hubs are 135 width. Alfine 11 one of those. [afaik]

I have a mountain climbing capability with an AW3 + a Schlumpf Mountain Drive,

a 2 speed planetary Crankset , Made in Switzerland.
so low range, offers the 3 hub gears another run thru.
Shift is internal, no change in the chain tension so no chain tensioner needed .

Herr Schlumpf also makes 2 overdrive cranks to use a small primary chainring set
the planetary multiplies the external cog ratio [1.65X or 2,5X]

I don't know anything about carver bikes, but you might be able to add an adapter to add a rear derailleur. Harris Cyclery sells an adapter claw.
https://sheldonbrown.com/harris/derailers-rear.html

Adapter also makes a IG hub + a double chainring crank work. Its a Kludge.
but note they assume you have a forward opening dropout, not a rear opening one.

And the frame lacks cable stops for gear cables.

you can use the greasy finger shifting between 2 chainrings.

Depending ont he hub you get, it might be cheaper to buy a budget frame and set up with a derailleur.

As for IGH, I have an 8 speed alfine and it is the bee's knees... and I am a big guy and very hard on parts. It has become my favourite bike over the past year.

What is the droput spacing on your bike? Carvers are mountain bikes, right? SO I would assume the spacing is 135mm, which fits Alfine and Nexus 8. If it is not 135 then you will need something else.

If you've got the dough, the Rohloff Speedhub is still the king of internally geared hubs... although setting up on a bike not designed for it is a little more work.

It might be possible to fit a derailleur if the dropouts are horizontal and not track ends. You can get derailleurs with a built-in adaptor claw, or just buy a claw to fit. However, the crankset/chainring will most likely be for 1/8" chain, so using an IGH will mean less new parts are needed.

Take it that this is a Original 96er. If so, you should have and EBB as well as two drive-side dropouts (one with a derailleur hanger and one without).

You should be able to go to you local Carver dealer and order the correct drive side dropout if you don't have the deraileur hanger one https://www.carverbikes.com/Dealers/#Auth

Forget the Brompton hub or Sturmy Archer, these are not appliciable for what is a pretty custom MTB, although Alfine 11 may work; but if you have the correct parts, a normal deraileur gear system should be easy to install.

If not, photos please to see what you have