All (I think?) the previous solutions don't work all that well in combination with coloured cell backgrounds: the backgrounds will stick out over the prettily rounded corners.
The solution is to apply clipping. And the difficulty with that is that the clipping path needs to be set before the table is drawn. A.f.a.I.k., the only way of achieving this is saving the whole table into a box first, then setting the clipping path accordingly. Just adding clip to the TikZ node didn't do it for me at least.
Since this amounts to quite a bit of boilerplate around the table, you could put the whole thing into an environment, and use the environ package to capture the table content conveniently.
\documentclass{article}
\usepackage[dvipsnames,table]{xcolor}
\usepackage{array}
\usepackage{environ}
\usepackage{tikz}
\newsavebox{\tablebox}
\definecolor{tablecolor}{named}{ForestGreen}
\NewEnviron{rndtable}[1]{%
\addtolength{\extrarowheight}{1ex}%
\rowcolors{2}{tablecolor!20}{tablecolor!40}%
\savebox{\tablebox}{%
\begin{tabular}{#1}%
\BODY%
\end{tabular}}%
\begin{tikzpicture}
\begin{scope}
\clip[rounded corners=1ex] (0,-\dp\tablebox) -- (\wd\tablebox,-\dp\tablebox) -- (\wd\tablebox,\ht\tablebox) -- (0,\ht\tablebox) -- cycle;
\node at (0,-\dp\tablebox) [anchor=south west,inner sep=0pt]{\usebox{\tablebox}};
\end{scope}
\draw[rounded corners=1ex] (0,-\dp\tablebox) -- (\wd\tablebox,-\dp\tablebox) -- (\wd\tablebox,\ht\tablebox) -- (0,\ht\tablebox) -- cycle;
\end{tikzpicture}
}
\begin{document}
\begin{rndtable}{l|l}
\multicolumn{2}{c}{\cellcolor{tablecolor}\color{white} Team sheet} \\ \hline
GK & Paul Robinson \\
LB & Lucus Radebe \\
DC & Michael Duberry \\
DC & Dominic Matteo \\
RB & Didier Domi \\
MC & David Batty \\
MC & Eirik Bakke \\
MC & Jody Morris \\
FW & Jamie McMaster \\
ST & Alan Smith \\
ST & Mark Viduka \\
\end{rndtable}
\end{document}
Looks like this:
