Center text in a single table cell

The error occurs because \\ is redefined by \centering (and other commands, such as \raggedright), but the problem only occurs for the final column. To fix it you can load the array package and add \arraybackslash after \centering in the cell, which restores the definition of \\.

Another option, mentioned by Gonzalo Medina in a comment, is to use \tabularnewline instead of \\ to end the row, which does not require array:

\x & \centering\y \tabularnewline

(The \arraybackslash command is simply defined as \def\arraybackslash{\let\\\tabularnewline})

Complete example:

\documentclass[12pt,a4paper]{book}
\usepackage{array}

\def\x{This is a paragraph of text that should be flush both right and left. Centering an adjacent cell should not cause this cell to be centered.}
\def\y{Centered text}

\begin{document}
\centering
\begin{tabular}{p{2in}|p{2in}}
\x & \centering\arraybackslash\y \\
% \x & \centering\y \tabularnewline  % alternative version of the previous line
\centering\y & \x \\
\x & \x
\end{tabular}

\end{document}

Add a multicolumn that spans a single column.

\documentclass[12pt,a4paper]{book}

\def\x{This is a text aligned according to column alignment defined in tablular.}
\def\y{Centered text}
  
\begin{document}

\begin{tabular}{l|l}
   \x & \x \\
   \x & \x \\
   \multicolumn{1}{c}{\y} & \x 
\end{tabular}
 
\endtabular}

\end{document}