For filling small(ish) holes I wouldn't feel bad using most any 2 part 1:1 clear resin. I've used whatever happens to be cheapest on amazon on a given day with no issues. At times I've bought a couple gallons, kept it in a closet in the house, and used it over a year or more with no issues at all. The very expensive stuff tends to be deep pour, which I don't think you have any reason for here.
If you just want something right now, you can get the Watco super glaze in clear at Walmart or Lowes or Home Depot. It's expensive by volume to buy it that way, though.
I would clean up and sand the interior of the cavities as best I could, perhaps with some small sanding sticks or similar, and then vacuum out any dust. You will then want to seal the grain in the cavities to prevent bubbles when you do your pour. I've "sealed" with poly, shellac, and a thin coat of epoxy resin. Doesn't seem to really matter and everything that builds a protective film seems to work, but if you don't seal you'll get tons of bubbles during your pour and for quite a while afterwards.
You can tint your epoxy in various ways, I normally use mica powder because people like that glimmer it gives in the type of product I do. For your purposes a dye may be better, but for black fine powdered charcoal or even graphite powder can make epoxy very dark. Whether you use powder or dye, a little goes a long way. Pigments CAN somewhat bleed into the wood at times so be careful.
When pouring you will want to mix the epoxy very thoroughly as that will also help prevent bubbles. A drill with a mixer is great if you're doing any quantity. Most of the time if I use epoxy it's for filling lettering in signs and plaques, which is essentially a similar application to what you're doing, except my cavities to receive the epoxy are cleaner cut as they're machined. If I'm just doing a little a solo cup and a popsicle stick with some elbow grease is good enough.
For small holes and cavities I use syringes to fill them so it doesn't get all over everything. I buy a quantity of syringes with plastic or metal barrels and treat them as single use. I normally remove the plunger and fill the syringe from the rear, as trying to suck it up with a vacuum from reversing the plunger is slow and causes bubbling.
You will want to hang out near your pours and watch them like a hawk for 15 or 30 minutes. You WILL get some bubbles, especially from a natural cavity. They're easy to handle, use a cheap blowtorch and wave it near them. That's all you have to do. I use a butane torch from harbor freight and cheap lowes butane. Just wave it near it, if you focus on a spot or let the flame hit it you may actually burn the epoxy. Oak in particular in my experience loves to give off bubbles, so you will want to watch it until the epoxy has at least began to set up. Depending on your sealing job and the size of the cavities you will probably need to add a small bit more epoxy after it sits for a while. Even after setting, if you scuff up the surface and pour on top it will blend fine. The issue is color matching the other cavities if you do this with a second batch of epoxy. Probably not a major issue with black.
It goes without saying but try to be in as dust free of an environment as possible. Also, even after it sets, it will take quite some time to cure fully. Resist the urge to handle it (and leave your fingerprints in it). Voice of experience here.
Sanding for removal of excess epoxy is quite difficult to do without also removing a lot of wood around the cavity, so be very careful. I recommend you try to get it as close as possible to perfectly even with the surface of the wood, or just a tiny bit proud. A hand plane can be good for this, but at the same time you'll have to do a lot of work sanding and polishing the surface of the epoxy if there is any "chatter". For a lot of the things I do the lettering or logos I fill don't need to be perfectly flat and some people like the "bubbled" appearance of a slightly overfilled cavity or the concave appearance of one that is slightly underfilled. However for a table I'm sure you want it flat.
Note also that epoxy is rather stinky. Also, if you feel the cup or bowl you mix it in getting hot, that is normal. The curing reaction is exothermic, and while it will cure somewhat faster in hot environments, it will happily cure even in humid areas without issue.
