I have a significant 2x2 interaction in a between-subjects design. I would normally report omega-squared as my effect-size measure, but I've been asked to provide Cohen's d instead? Can Cohen's d be computed for an interaction? If so, how?
You can translate pretty much any of the effect sizes to Cohen's d, so start with omega and work your way over. Equations are available for them all online... the wikipedia page for effect size is good for this.
In your particular case though you can get a numerator for cohen's d as (a1 - b1) - (a2 - b2). That's the simple effect of a 2x2 interaction with,
b as the variables (e.g. sex and handedness) and the numbers are levels of the variables (e.g. male / female and left / right). Your denominator is just the square root of the MSE from the ANOVA*.
*assuming homogeneity of variance