APA6 Class - Single-spaced Tables for Manuscript

apa6 does not a provide a float-specific spacing as a document class option (see section 3.1 Class Options of the apa6 documentation, p 2). However, it loads the etoolbox package by default which provides \AtBeginEnvironment{<env>}{<stuff>} that hooks into and adds <stuff> at \begin{<env>}. So, you can use

\usepackage{setspace}% http://ctan.org/pkg/setspace
\AtBeginEnvironment{tabular}{\singlespacing}% Single spacing in tabular environment

Although it is not necessary to load use the setspace interface for \singlespacing in this case, it is just for convenience. If you're not allowed to use setspace, you could also just use

\makeatletter
\AtBeginEnvironment{tabular}{%
  \def\baselinestretch{1}\@currsize}%
\makeatother

Here is a minimal example using the former setspace adjustment:

\documentclass[man,floatsintext]{apa6}% http://ctan.org/pkg/apa6
\shorttitle{Some title}% Dummy title
\usepackage{lipsum}% http://ctan.org/pkg/lipsum
\usepackage{setspace}% http://ctan.org/pkg/setspace
% Already loaded by the apa6 documentclass...
% \usepackage{etoolbox}% http://ctan.org/pkg/etoolbox
\AtBeginEnvironment{tabular}{\singlespacing}% Single spacing in tabular environment
\begin{document}
\lipsum[1]
\begin{table}[ht]
  \begin{tabular}{ccccccc}
    \toprule
    One & Two & Three & Four & Five & Six & Seven \\
    \midrule
    100 & 200 & 300 & 400 & 500 & 600 & 700 \\
    100 & 200 & 300 & 400 & 500 & 600 & 700 \\
    100 & 200 & 300 & 400 & 500 & 600 & 700 \\
    100 & 200 & 300 & 400 & 500 & 600 & 700 \\
    100 & 200 & 300 & 400 & 500 & 600 & 700 \\
    \bottomrule
  \end{tabular}
  \caption{This is a table.}
\end{table}
\end{document}

lipsum was merely used to create dummy text Lorem Ipsum style.