I want to strip and refinish this coffee table. I don't have an orbital sander, the tools I have are belt sander, a vibrating sander or by hand.

I intend to stain it this color
I want to strip and refinish this coffee table. I don't have an orbital sander, the tools I have are belt sander, a vibrating sander or by hand.

I intend to stain it this color
Can you? Sure!
Should you? Well...
crip659 made a really good point that if this is a veneer, then a belt sander will go right through it in no time. Additionally, if this is a laminate (with a picture of wood printed on it) then what's underneath is likely to be particle board and you won't like the look of that at all. It's a really good idea to make sure you know what you've got before you get started.
A belt sander tends to be a very aggressive tool that's really efficient at removing a lot of material very quickly. Can you use it to remove the finish, absolutely you can, but be very careful that you don't accidentally go through the finish and dig into the part you're looking to keep.
You'd probably want to start at a higher grit paper than you'd normally think, just because the belt sander is so aggressive. If you find that, say 120 grit paper just isn't making progress, you could step back down to 80 grit, but if you start at 40 grit, you're going through your finish before you know it and you're making divots in your table top.
Also, a belt sander will not get into the little nooks and crannies. You will have to use another method (like hand sanding) to get those.
As a thought, consider chemical strippers. The worst the stripper is for you and the environment, the better it is on removing the finish. However, there are a number of reasonably friendly strippers that are reasonably decent at actually getting the finish off, too. Chemicals are also really good at getting to the inside corners of joints and into decorative details to remove the finish without sanding them out of the piece.
Once you've used chemicals, it may be a bit of hand sanding to finish things off.
Finally, I'd suggest you take a look at the Woodworking sister site for a ton of info on refinishing.
A vibrating sander will work and so will doing it by hand with a sanding block. You'll want to stay away from the belt sander. They remove a lot of wood even with fine grit sandpaper and are not friendly to control on something as fine as a table top. You might want to look into some of the paint and finish strippers out there. They've come a long way in making them user friendly.
I would not sand it.
Get your hands on some Howards Restor-a-Finish in a dark tint, which might be all you need. You can use fine steel wool on your first pass.
If that doesn't cut it, get citrustrip. You won't need a super powerful stripper to get that layer of finish off.