natural VIBRATO comes aboot when you've worked and built up your DIAPHRAGM.
I first tried this method in high school chorus class. my music teacher showed me how.
here's how I do it.
useing your pianner or keyboard or even your axe finde middle C.

this middle C note may be too low for some of you so go up a whole step to D or up even another whole step to E.

just whatever feels comfortable to you.

 finde this note and strike it and holde it and match your voice to the note much like you'd tune two strings together.
 you'll feel the two notes HARMONISE when you match the note.
something I like to do is match my voice to the sound of the LAWNMOWER while I'm mowing grass. no one can hear you and it passes the time.

open your mouth(jaw) makeing an "O" shape, keeping your tongue flat to the bottom of your mouth.  ohhhhhh.
strike the note and holde it, vocalise the note and holde it and then keep pushing the air from your lungs until you have no air left(DO NOT TAKE A BREATH)
 keep pushing the note until you run completely oot of air( THIS IS IMPORTANT-don't inhale) and KEEP PUSHING the note until you make a little croaking noise.
sometimes I'll blow out most of my lung air and then begin. this is a quicker way for me.
 
 REPEAT this excercise a couple of times and THEN go up a whole step and begin again.

 do this a few times and keep moveing up a whole step at the time until your voice  begins to crack and you cannot sing any higher.  you may wish to go up HALF steps as you reach your upper range.

Then go DOWN a couple of  whole steps from where you left off when you voice "began" to crack and begin again, makeing an O shape with your mouth. ohhhhhh!
 repeat until you again reach the TOP of your range.
 as you CORRECTLY do this vocal excercise you'll feel your diaphragm muscle and begin to experience VIBRATO in your voice.

do the entire excercise at least a few times  a day and have fresh cool water handy to sip on.
 
I do this in the van on the way to a show matching my voice to the whine of the tires or motor and by the time I get to the place I'm all warmed up and ready to go.

I also do this excercise before I record vocals.
 This method Works for me and it WILL work for you.
your diaphragm will be stronger and you'll increase your vocal range too.

this excercise will help anyone who tries it.
if you have ANY QUESTIONS uh, SING OUT and I'll try to explain any points you may not be clear on.

thanks for lettin me share and I hope this helps you cats and dogs.
RLS