Either way, I think we need clarification once the OP knows what exactly it is they want, AND can come up with more budget.
Anodizing is doing this intentional oxidizing process and then treatment. While in a certain state, the metal can be colored through the use of dyes and then sealed. This process is repeated to get different colors. Costs can run from $50 on up.
Painting is the application of paint to the yoyo. Any number of types of paints can be used, but the consensus seems to be that automotive paint has the best results as far as finished product and durability. However, this product, no matter now nice, is going to ship, crack, scratch, flake and peel away in time. All you can do is postpone this from happening. Expect prices of $25 and up, with $50 and up being more realistic.
Powder Coating is applying a powdered plastic material via static charge. I forget if the metal is charged negative or positive, but the powder is charged the opposite. The material is coated and placed in an oven, which melts the powder into a coat. Some formulations can be textured. This tends to be very durable and difficult to damage and remove, but it can be done. It won’t protect your yoyo from damage, but the odds are the powder coat will dent with your yoyo, so at least that dent will look uniform! The requirement of specialized equipment will keep costs high, but these can be crammed in with other jobs as part of a batch and as such can keep costs reasonable. Odds are any motorcycle, auto or other service shops that do body work can recommend a place that can do this.