Specify a static id to your classic reports; for example, specify parent for parent report and child for child report.

Then add the following CSS in the page’s CSS inline section:

#report_parent td.t-Report-cell {
  background-color: aquamarine;
}
#report_parent thead {
  background-color: black;
}

You can notice in the above CSS that I have added the “report_” before the static id because for the column section; it automatically added the “report_” in the background.

Similarly, apply the CSS for child report:

#report_child td.t-Report-cell {
  background-color: aquamarine;
}
#report_child thead {
  background-color: black;
}

Try this and let me know.