Hm. I've always been able to do vibrato so I dunno how much I could help you. But I'll give it a shot.

First of all, I would suggest you identify what kind of vibrato you want to do. Listen to your favourite singers and visualise what they do. If you're into rock and metal you'd probably want a mix of pitch and volume. That is the type I do and the mix depends on the sound I want to go for.

The first thing to consider is for vibrato to work properly, especially pitch vibrato, you need your voice to be relaxed. That is especially true for pitch vibrato, you can't "shake" a note you have a death grip on. Support the note to relieve the tension off your throat first. Same thing with volume/stomach vibrato, if your lower body is incredibly tense, good luck pulsating your air supply without breaking. I personally get those problems high in my range.

Next you need to practice what you actually do. Grab a metronome and set it at some ridiculously slow tempo, like 40BPM. Sing a tone in some comfortable range and on each beat, raise it (or drop it) by some interval, say a semitone, then on the next beat return to the original note. Once you have the hang of it, speed it up. You can make the transitions smoother by sliding instead of sharply switching. Focus on keeping it consistent, if it wobbles it won't sound good.

Stomach vibrato is a bit more difficult, for me at least. You sing a note and alter the volume by either dropping or increasing your support. The problem is, if you try this slowly you don't really get into the right pattern. I can't remember right now but I think Jaime recommends saying "Hey" over and over again, then switch to a "HeyEyEyEyEy".

Good luck!

BTW, as far as I'm aware, "natural vibrato" is a mixture of stomach and pitch.

Pitch vibrato is essentially the vibrato of choice. Work with a metronome, it helps!

Well, pitch vibrato should be the base but volume fluctuations on top of it enrich it into a more professional sound.

Most people will, once they have removed excess tension from their singing, develop a natural vibrato, but this isn't true for everyone.
I'd pretty much eliminated vocal tension, but still didn't have a vibrato, but this is fine. It's quite an easy technique to teach yourself, but it takes time.

The most common vibrato is the pitch vibrato, which is usually sung at a rate of between 5 and 7 per second. 6 being the typical rate.

A good place to start is at about 80bpm, doing 2 per beat (For example C,B,C,B for each beat). This should be fairly easy for you. If you're having trouble keeping time, putting your metronome into quaver mode should help.

It's important to stress the change in tone is from the vocal cords, and doesn't come from using your stomach. It shouldn't be pushed.

Now all you need to do is slowly work your way up.
120 is the equivalent of 4 per second, 150 is 5 per second and 180 is 6.

Just keep it easy and relaxed, and when you get to about 140bpm, you will notice it starts to feel a lot easier and more natural.

It will take time, but it's worth it.

When you have this foundation, you can experiment a bit with different vibrato methods, such as "stomach vibrato". In truth, it's more of a tremolo than a vibrato, but can sound very good if done right.
I've found that if learnt before pitch vibrato, it can become a bit of a crutch.
I know it did for me.

Also, Brett Manning does a great vibrato course, but it's a bit pricy.

Good luck, and let us know how you get on

I could do pitch vibrato naturally long before I learnt how to do stomach vibrato. The thing is, pure stomach vibrato sounds a bit ****ty if you ask me. If your voice is free, it typically wants to drop in tone as you drop your support on each "iteration" of stomach vibrato. You can either focus to counter that, or you can exploit it by pushing it even further in that direction. The result is a pitch vibrato with simultaneous tremolo, which sounds much more powerful than just pitch. You can hear many singers doing exactly that, Dickinson being a prime example.

Natural vibrato only comes when your voice is fully relaxed and and can resonate freely. The slightest tension with impede on it on slow it down to a wobble. Don't worry to much about it. Practice your voice placement and your proper jaw opening to create sufficient place for the voice to vibrate and it will come.

Thanks for good advices. Maybe I shouldn't worry about this too much as I still have more critical issues like intonation.

I don't mean to say that I have great vibrato, but to me, it's almost natural. I don't really practice it, it just happens when I sing.. it's a natural reaction when I sustain notes. But when I do the pitch vibrato exercise, it does warm-up it a bit well.