Why let guitar players have all the fun?
The way many keyboard players add vibrato is to turn up the mod wheel, and inject some LFO to change the oscillator pitch periodically. That’s fine, but consider guitar players—they add vibrato by moving their fingers on strings, which can give a more human quality than using an LFO.
So, try your hand (get it?) at doing vibrato with your fingers instead of using the LFO. This also frees up the mod wheel to do other, perhaps more interesting changes (see Get Imaginative with the Mod Wheel). The image at the top shows what finger vibrato looks like after it follows an upward bend.
For the most realistic guitar-style bending, remember to bend up, not down—strings can only bend up, unless you’re using a vibrato tailpiece that can shift the pitch up or down.