You can try something like this, but use white (and smaller size) LEDs instead of colour changing ones.
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You could do something with Christmas tree lights but it might be better to find one of those fiber-optic lamps where it is a bunch of thin fibers in a bundle that spread out from the middle. The light would not be as obtrusive as a lightbulb and might be easier to glue or tack on along the length of the centerpiece branches. Even a flashlight fiber-optic toy might work so you can imbed that standalone in your centerpiece without the need for electrical wiring. Good luck.