From UD, right outside the city.
Well, as a basic plan you would need a page for them to click on the name. Perhaps instead of a list of all the kids, you give each parent a unique code to enter, which would correspond to their child. When they enter that code, they are taken to a page that shows them the disclaimer and has a text box for them to fill out. When they submit that, you would store the name they typed in the database, tied to the child.
So, page with a textbox for the unique code.
waived (this would be a flag to set if the parent had submitted the waiver)
text (what they enter in the waiver textbox)
childID (the ID from the child table corresponding to their child)
when they submit, page pulls the child data from the child table corresponding to the specific code.
parent sees the info, reads the waiver, types their name, submits
page sends the parent's "signature" to the DB and stores in a new parent row, along with the child's ID.
Additionally you could add another page for the coach to see which kids' waivers had been signed.
Does that make some sense?
I'm no lawyer, but this scheme seems like it would hardly hold up against a lawsuit...how can you prove the parent is the one who typed those words in. You might want to take the IP address of the parent down as well. :\