Q: How do I obtain good vibrato?

The classic way to get it is to imitate, like when you were a kid, a
rapid fire machine gun. Then do it inhaling instead of exhaling. It’s
the same throat motion that gets the throat vibrato.

What I personally found to work (not "classic" how-to) is to
bend the 3 draw about a 1/2 step, then put vibrato in. Your throat is
involved getting the bend, so there’s some feel there before you go for
the vibrato.

But, try the machine gun thing.

The vibrato is definately a combination of a strong staccato and a steady
bend. You should first practice and develope a steady staccato. Without
the harmonica, purse your lips and cough lightly as though you are clearing
your throat. The air expelled must have the sensation of coming from the
back of your throat. The next step is to practice with the harmonica.
Each cough, or burst, equals 4 beats per measure, hu hu hu hu. When you
can do this, then double the speed doing 8 beats per measure, huhu huhu
huhu huhu. When this becomes easy increase it to 16 beats per measure,
huhuhuhu huhuhuhu huhuhuhu huhuhuhu. If you practice this you will have
a strong staccato. The last step will be to impose the bend during the
staccato. After developing the vibrato you may then want to smooth it
out by softening the staccato or slowing it down.

The staccato is distinct breaks between successive notes. When adding
the bend, these breaks are eliminated by the steady air flow and the result
is that the staccato coughing tends to vary the bend causing the bend
to waver slightly in pitch. If observed on a meter this fluxuation is
apparent.

Although my forte is really not playing but rather making special harmonicas,
repairing and rebuilding the chord and the harmonetta, I did develope
the vibrato and would like to help others if I can.