A limit on your available time is going to be a put a downer on the internship prospects..
I hired an 18 year old a while back, when ever I call and ask if he is available - he pretty much says - "Yep!"
But I have to seriously question one part of your opening post... When you say you could only do evenings and weekends.. at this late stage in your studies - do you really have to attend college 9-5? five days a week? Or is this a work schedule you have set for yourself? Cause I thought you doctorate types just cycled in about once a week wearing a scarf and had a 1/2 hour chat with a tutor in a garish sweater, hush puppy's & corduroy trousers.. and then spent the rest of the time at home banging away at a laptop doing the "thesis" ....

Hmm er.....bio chemistry eh.. perhaps there is a lot of practical stuff you need to do for that?..er...
If you ARE in charge of your own schedule - then I would offer the studio this -
'flexi time' - two sold days (24 hours per day if required!) per week (any days - they pick them according to the studio diary & when they need your help) + the willingness to "drop stuff" - if they really need you on an important session to do 3 days, even 4.
That's pretty much the deal I have with my intern, (different situation obviously) he's in a recording / media course - but his tutors know that he's really learning the sh!t when he is on real sessions - so they cut him some slack if he needs school days off (he attends school Wednesday, Thursday and Friday) If we are quiet I like to get him in at least one day to keep the place tidy + he's always nipping in to work on his course work projects etc in down time / weekends..
I would not suggest you offer 'half days'(evenings only) to them. Or ever give the impression that "weekends may be a problem"
But see what others say here and obviously, do what you think is best for you and your situation,
Good luck!