Let $M$ be an $n$-manifold endowed with a nonvanishing $n$-form $\Omega$, let $\mathrm{Diff}(M,\Omega)$ denote the group of $\Omega$-preserving diffeomorphisms of $M$, and, for $x\in M$, let $\mathrm{Diff}(M,\Omega,x)$ denote the subgroup that fixes $x$.
Your question, then, easily reduces to "Is the homomorphism $D:\mathrm{Diff}(M,\Omega,x)\to \mathrm{SL}(T_xM)$ defined by $D(f) = f'(x):T_xM\to T_xM$ surjective?"
The answer is 'yes'. The reason is that the image of $D$ has to be a Lie subgroup of $\mathrm{SL}(T_xM)$, and it is very easy to see that it contains a neighborhood of the identity in $\mathrm{SL}(T_xM)$. Consequently, it must be all of $\mathrm{SL}(T_xM)$.