When I use [shrink], I lose vertical centering. How do I get my stuff shrunk and centered?

You could wrap the table in \resizebox from the graphicx package.

\documentclass{beamer}
\usepackage{booktabs}
\usepackage{graphicx} % loaded by beamer, but included here for explicitness
\begin{document}
\begin{frame}{Correlations between Harm, Unfairness and Disgust} 
\begin{center}
\resizebox{\textwidth}{!}{%
  \begin{tabular}{lllllllll} 
    \multicolumn{8}{l}{\textbf{Table 3.} All possible regressions of harm, unfairness, and disgust predicting punishment} \\ 
    \toprule 
    & M1 & M2 & M3 & M4 & M5 & M6 & M7 \\ 
    \midrule 
            Harm & .35 (.01) & & & .20 (.15) & & .24 (.07) & .14 (.31) \\ 
            Unfairness & & .41 (.01) & & .31 (.02) & .34 (.01) & & .28 (.04) \\ 
            Disgust & & &.34 (.01) & & .23 (.07) & .25 (.05) & .19 (.13) \\ 
            R$^2$ & .12 & .11 & .11 & .20 & .17 & .17 & .22 \\ 
    \bottomrule 
    \multicolumn{8}{l}{Note: Standardized beta coefficients, with p value in parenthesis} \\ 
 \end{tabular}}
\end{center} 
\end{frame} 
\end{document}

You can use a minipage with a predefined height and optional positioning arguments c to force vertical centering:

\documentclass{beamer}
\usepackage{booktabs}

\begin{document}

\begin{frame}[shrink=35]{Correlations between Harm, Unfairness and Disgust} 

\begin{minipage}[c][1.3\paperheight][c]{\textwidth}
  \centering 
  \begin{tabular}{lllllllll} 
    \multicolumn{8}{l}{\textbf{Table 3.} All possible regressions of harm, unfairness, and disgust predicting punishment} \\ 
    \toprule 
    & M1 & M2 & M3 & M4 & M5 & M6 & M7 \\ 
    \midrule 
            Harm & .35 (.01) & & & .20 (.15) & & .24 (.07) & .14 (.31) \\ 
            Unfairness & & .41 (.01) & & .31 (.02) & .34 (.01) & & .28 (.04) \\ 
            Disgust & & &.34 (.01) & & .23 (.07) & .25 (.05) & .19 (.13) \\ 
            $R^{2}$ & .12 & .11 & .11 & .20 & .17 & .17 & .22 \\ 
    \bottomrule 
    \multicolumn{8}{l}{Note: Standardized beta coefficients, with p value in parenthesis} \\ 
 \end{tabular} 
\end{minipage} 
\end{frame} 

\end{document}

Rather than shrink or resize the entire tabular environment, which may render its real contents (the numbers) barely legible, it may be preferable to reduce the amount of inter-column whitespace selectively, by reducing the value of the macro \tabcolsep; the edited MWE below reduces its value from 6pt (the default) to about 4.5pt, while also setting the fontsize to \scriptsize. (In addition, I've taken the liberty of applying a few stylistic changes here and there, e.g., replacing \toprule and \bottomrule with \midrule[\heavyrulewidth] in order to get better spacing to the adjacent text, and a bit more vertical separation before the $R^2$ line. Finally, I've also replaced tabular with tabular* in order to get a table that occupies the full \textwidth.)

By the way, I can't help but remark on the fact that the frame's title includes the word "correlations", whereas the table's caption and legend refer to regression coefficients rather than correlation coefficients. Might this discrepancy cause some puzzlement or resistance among the members of your audience?

\documentclass{beamer}
\usepackage{booktabs}
\setlength{\tabcolsep}{4.45pt}
\begin{document}
\scriptsize
\begin{frame}{Correlations between Harm, Unfairness and Disgust}

\begin{tabular*}{\textwidth}{@{}l@{\extracolsep{\fill}}*{7}{l}@{}}
\multicolumn{8}{@{}p{\textwidth}}{\textbf{Table 3.} All possible regressions 
  of harm, unfairness, and disgust predicting punishment} \\
\midrule[\heavyrulewidth]
    & M1 & M2 & M3 & M4 & M5 & M6 & M7 \\
\midrule
Harm       & .35 (.01) & & & .20 (.15) & & .24 (.07) & .14 (.31) \\
Unfairness & & .41 (.01) & & .31 (.02) & .34 (.01) & & .28 (.04) \\
Disgust    & & &.34 (.01) & & .23 (.07) & .25 (.05) & .19 (.13) \\[1.5ex]
$R^2$      & .12 & .11 & .11 & .20 & .17 & .17 & .22 \\
\midrule[\heavyrulewidth]
\multicolumn{8}{@{}l}{Note: Standardized beta coefficients, 
  with p values in parentheses} \\
\end{tabular*}
\end{frame}
\end{document}