Singers who have good coordination of breath and open space usually have vibrato which you can imitate. Think of a singer (probably someone you’ve heard singing opera or classical music) who makes a huge sound when singing. Now imitate that singer.
Find a quiet place where you can make plenty of sound. Hear the singer’s voice in your mind and then imitate that singer. If it helps, open your arms wide, hold a towel, or stand on a chair, so you feel enormous. Imitating someone with good technique doesn’t hurt your voice. You may discover that you can make some pretty big sounds yourself.
If you imitate a singer with vibrato, you can probably figure out how to imitate that vibrato, too. When you do, continue to explore that sound and notice what your voice sounds like. You can even record yourself, just to prove that you made that much glorious sound.
If you didn’t find a different sound, imitate a different singer. This time choose a larger-than-life opera singer. Be flamboyant and pretend that you’ve been called in to sing because the star is ill. Fake it and sing some of this singer’s songs — even make up the words.
The key to singing with vibrato is to make the sound happen naturally — don’t force it. Explore different kinds of sounds, and work with space and breath to find vibrato.
You may be tempted to create vibrato by bouncing your abdomen or your larynx — but don’t. Bouncing your abs or larynx doesn’t consistently produce vibrato; instead of forcing it, let the vibrato happen because you keep air consistently flowing. Ham it up and enjoy vibrato!