You could define a new length to store the width of the longest verse and use this length as a \parbox
's width to be centered using a center
environment:
\documentclass{article}
\usepackage{lipsum}
\newlength\mylen
\settowidth\mylen{bbbbbbbbbbbbbbbbbbbbb}
\begin{document}
\lipsum[1]
\begin{center}
\parbox{\mylen}{aaaa \\
bbbbbbbbbbbbbbbbbbbbb}
\end{center}
\end{document}

Another option would be to use the verse package and its facilities:
\documentclass{article}
\usepackage{verse}
\usepackage{lipsum}
\begin{document}
\lipsum[1]
\settowidth\versewidth{bbbbbbbbbbbbbbbbbbbbb}
\begin{verse}[\versewidth]
aaaa \\
bbbbbbbbbbbbbbbbbbbbb
\end{verse}
\end{document}
If you want each verse to appear centered in its own line, you could simply use a center
environment:
\begin{center}
तपः स्वाध्याय निरतम् तपस्वी वाग्विदाम् वरम् | \\
नारदम् परिपप्रच्छ वाल्मीकिः मुनि पुंगवम् ||
\end{center}