Yes, unless I misunderstand you.
title:whateveryouwant
tags:colortabs
<<tabs "one two three four" "one">>
<style>
.tc-tagged-colortabs .tc-tab-buttons button:nth-child(1) {background:blue;}
.tc-tagged-colortabs .tc-tab-buttons button:nth-child(2) {background:green;}
.tc-tagged-colortabs .tc-tab-buttons button:nth-child(3) {background:yellow;}
.tc-tagged-colortabs .tc-tab-buttons button:nth-child(4) {background:red;}
</style>
The reason you need the tag "colortabs" is to prevent the styling from affecting all tabs in the TW. Instead you can then use .tc-tagged-colortabs to limitit it to that particular tiddler.
Generally, you'd not want to put the styles in the tiddler itself but in a separate stylesheet tiddler, i.e any tiddler with the tag "$:/tags/Stylesheet". And you omit the <style> tags there, just put the lines starting with .tc-tagged..... etc
<:-)