Depending on the tests you used, I might be concerned about the lack of normality. If the original tests are iffy the multiple comparisons can't be any better. Can you provide more details on tests, sample sizes, etc? best wishes.

Thanks for your reply. 

There are numerous dependent variables (ratings made by the participant), and 4 independent variables. I have carried out one regression for each DV, with all regressions having the same 4 independent variables. The sample size is about 150 participants.

Regarding normality - for some of the variables, a normal distribution would indicate that the participants had been doing the task wrong, as their ratings should tend towards one end of the scale. (The scale goes from 0 to 100). An example of a ratings scale (which isn't used in my study but is comparable) would be 'how disgusting do you find this image?', and show them a very disgusting image, or an image that isn't disgusting to most people. The scores will naturally tend towards high or low depending on the image, but that means the scores will not come out as normally distributed. 

I have been thinking about how regression doesn't require the DV or IVs to be normally distributed, only for the residuals to be normally distributed. My residuals are pretty normal, so perhaps I don't need to use confidence intervals?

I guess by statistical tests you mean different regressions with those 4 independent variables. Do you have other tests?

What is your aim of using confidence intervals?

If it is just because your data is/not normal then it is futile. You could give confidence intervals in any case.

For nonnormality,  a linear model will hold unless residuals are normal and homoscedastic. You say the residuals are normal, check also homoscedasticity.

Correction for multiplicty might be done using multivariate regression analysis. I do not know number of dependent variables, but if they are not too many multivariate regression is usable. Also canonical correlation analysis should give you some ideas.

Coming back to BH procedure, beside the standard function p.adjust in R I found the following page that talks about other alternatives

http://strimmerlab.org/notes/fdr.html

and another package which is not mentioned in the above link

https://cran.r-project.org/web/packages/mutoss/mutoss.pdf

I could not find an implementation in R of reference you mentioned for confidence intervals.

Elizabeth,

Could you please share a tips about how you carried out the procedure of the adjustment of confidence intervals with FCR (Benjamini and Yekutieli, 2005)?

I have the same problem as you describe in your question. No place to find a description of the method for non-statistician.