I think you already pretty much summed it up.
You are applying for the position because it sounds like exactly what you have been looking for.
You have x, y, and z skills to offer, (mention some things they are asking for) and the position fits perfectly with your schedule.
You feel you are a worthy candidate as you would be an asset to them and look forward to hearing from them.
Thank them in advance for their consideration.
Sincerely.....
Keep the cover letter short and to the point.
Don't rehash everything on your resume.
Tailor it to what they are looking for and briefly explain why you'd be a great fit.
Very best wishes!
Edit: After reading a previous response, I just want to say that it's not always a bad thing to mention that something fits your schedule.
Many people have a standard cover letter that they send out to multiple employers.
If this position really seems like a perfect fit, I don't see the problem in mentioning it. It could be another plus for you.
Believe me, in HR and involved in hiring, it never fails...
You advertise a part time position from 1-4 on Tuesdays and Thursdays and you get 30 people who apply that can only work Noon-2 on Mondays and Wednesdays or every third Friday and they don't tell you that until the interview. They hope the job will change to their schedule, not the other way around.
Flexibility is very important. More so on the applicant's part, not the employer's, when you're trying to get a job.
If you are available the hours they specifically outline that they need someone, I don't see harm in letting them know up front that is not going to be a problem.
Again, just my opinion.