Not sure if you are still looking for an answer to this question. The standard overexpression method in zebrafish is mRNA injection into one cell stage embryos. This would cause global over-expression and you can titerate mRNA concentration injected till you see a specific overexpression phenotype with little or no toxicity from the mRNA injection itself. Use GFP/mCherry mRNA at same conc as a control. A variant of this would be to inject in one cell at 2, 4, 8, 16, 32 or 64 cell stage. As you can imagine this progressively gets difficult. If you want tissue specific and temporal overexpression, you can use GAL4-UAS system used extensively in Drosophila but also successfully in zebrafish. Temporal global induction can be achieved by using heatshock promoter driven constructs. This is a vast topic and a comprehensive discussion would form a book chapter. There is plenty of literature out there on how to achieve this. Happy to help if you have specific questions after that.
To my knowledge, one method that can do the overexpression method in zebrafish is mRNA injection into one-cell stage embryos. This would result in global overexpression. You could increase the mRNA concentration injected until you see a specific overexpression phenotype with little or no harm from the mRNA injection itself.