Hello there,
The antioxidant effects of various fruits are certainly a fascinating topic of study, so I'm sure you can put together an interesting project on this subject.
The browning reaction that goes on in cut apples exposed to the air is an easy assay for anti-oxidative activity, although it has certain drawbacks as well. You can read a short intro to the science behind apple browning here:
http://www.scientificamerican.com/artic ... turn-brown
Your concern about the red color of the juices making it harder to interpret the effects on apple browning may be justified. This is something you might just have to try and see. Do you have a plan for how you are going to quantify the "brownness" of the apple slices? If application of juice does cause a change in the reading of the fruit's darkness, perhaps you can just take a baseline reading immediately after adding juice and then again at the final time point, subtracting the two values to determine the total increase in brownness. Another option might be to use essential oils derived from the fruits of interest, or some other (colorless) extract or preparation thereof.
In addition to the apple browning test, there are many chemical tests that can be used to measure different kinds of oxidative chemical changes or kinds of antioxidant activity. There are a great many scientific studies published every year that address the antioxidant properties of various natural substances, so you may with to read some of these to get a feel for the different "kinds" of antioxidant properties peoples test for, and what kind of tests may be involved. Some of them may be simple enough that you could perform them with equipment you may have access to at school or home. As an example of the kind of journal article you might find useful, here's one I found by searching for "antioxidant juice" in PubMed Central, which is the NIH repository of open-access biology articles.
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2636748/
http://www.ncbi.nlm.nih.gov/pubmed/19770018
In the case of apple browning, the oxidative event that you are observing is the enzymatic oxidation of polyphenols by polyphenol oxidase. You might be interested in looking at other kinds of oxidative reactions, and at various ways that juices exert antioxidant effects. For example, does the protective effect of a particular juice come from its acidity? (If so, neutralizing the pH of the juice would lower the protective effect) Does it come from an enzymatic activity in the juice? (Maybe you can denature the enzymes with heat to inactivate them?) Does it come from pulp, or juice, or rind? (You could try different fractions of the fruit in your tests) Etc. There are many interesting questions you could ask, depending on your interests and on the kinds of assays you decide to run.
Good luck with the project!
-Will