  Let $\mathbf{k}$ be a fixed field of arbitrary characteristic, and let
$\Lambda$ be a finite dimensional $\mathbf{k}$-algebra. Assume that $V$ is a
left $\Lambda$-module of finite dimension over $\mathbf{k}$. F. M. Bleher and
the author previously proved that $V$ has a well-defined versal deformation
ring $R(\Lambda,V)$ which is a local complete commutative Noetherian ring with
residue field isomorphic to $\mathbf{k}$. Moreover, $R(\Lambda,V)$ is universal
if the endomorphism ring of $V$ is isomorphic to $\mathbf{k}$. In this article
we prove that if $\Lambda$ is a basic connected cycle Nakayama algebra without
simple modules and $V$ is a Gorenstein-projective left $\Lambda$-module, then
$R(\Lambda,V)$ is universal. Moreover, we also prove that the universal
deformation rings $R(\Lambda,V)$ and $R(\Lambda, \Omega V)$ are isomorphic,
where $\Omega V$ denotes the first syzygy of $V$. This result extends the one
obtained by F. M. Bleher and D. J. Wackwitz concerning universal deformation
rings of finitely generated modules over self-injective Nakayama algebras. In
addition, we also prove the following result concerning versal deformation
rings of finitely generated modules over triangular matrix finite dimensional
algebras. Let $\Sigma=\begin{pmatrix} \Lambda & B\\0& \Gamma\end{pmatrix}$ be a
triangular matrix finite dimensional Gorenstein $\mathbf{k}$-algebra with
$\Gamma$ of finite global dimension and $B$ projective as a left
$\Lambda$-module. If $\begin{pmatrix} V\\W\end{pmatrix}_f$ is a finitely
generated Gorenstein-projective left $\Sigma$-module, then the versal
deformation rings $R\left(\Sigma,\begin{pmatrix} V\\W\end{pmatrix}_f\right)$
and $R(\Lambda,V)$ are isomorphic.
