pH meter would be the preferred way to go, so if you can't use one I am afraid there is not much that can be done.
Trick is, most of the ways of remove the coloration require adding something, and most of substances that could remove color (like bleach) will change the titration result (bleach is basically a NaOH solution saturated with Cl2, it easily destroys most colored compounds, but you will be titrating the NaOH added, not the original sample).
Perhaps - but that's just a wild guess - adding activated charcoal would remove the coloration without changing solution acidity.
That being said - what do you hope to measure with the acid/base titration? Perhaps it is just that the titration is a wrong method selection?