The Greater Middlesex County schools post their athletic schedules on this site:
Please click on link then enter the school name you would like schedule for in blue line that says NEW! View Your School’s Customized Scores & Schedule Page: about 1/3 down the page. Below is a screen shot of where to enter the school name.
Some schools are using RSchool Today. Their links are below.
South River’s schedules can be found here.
Perth Amboy’s schedules can be found here.