I too did poorly on the SAT verbal but managed to do well on the MCAT verbal... at least well enough to get me accepted to medical school. The biggest difference is that the MCAT is all reading comprehension. There are no antonyms, analogies, or other similar types of questions. Have your cousin start reading... lots of reading. Relevant and pertinent to the MCAT things like science magazines, journals, newspaper editorials, etc. This will not only improve her reading speed, but will get her more adjusted to the types of material on the MCAT verbal. In my studying for the MCAT, I realized my success lay in being able to identify the major point(s) of each passage. Once I was able to critically analyze the main theme of the passage, it seemed as if the questions seemed to feed off of that in one way or another. When your cousin is "practice" reading different material, have her do the same for them as well. This way she will develop a critical reasoning ability for everything she reads. MCAT verbal passages are not light enjoyment pieces. They should be looked as problems to be solved. If she can master this now, studying for the MCAT will be much easier.
I realize there will be hundreds of other successful ways to study for the MCAT verbal, but this is what worked for me. Also, have her try different strategies everyone else suggests you and then of course go with the one (or combination of those) that work best for her.