Customize 2nd Row in a New Table Style

I think it you're on a subscription plan then upgrading to RH2020 is included. Otherwise you'll need to purchase a subscription to get the new version.

Is it important the second row is part of the style?

If not, simply select the second row of the table in author view and in Properties > General > Background you can apply a colour in that specific table.

I can't see any way in editor to do it, but you can do it in the code view.

First, remove the background-color setting for First Row using the editor. Then switch to the code view and add the following:

table.Mytablestylename tr:nth-child(1),
table.Mytablestylename tr:nth-child(2) {
background-color: pink;
}

Change 'Mytablestylename' to match your table style. and 'pink' to whatever colour you need for the top two rows.

Note: In RH2019 New UI Update 12 style editor, you won't be able to see that the above styling exists. I'm not sure if that is different in Update 13 or 14, or in RH2020.