Create DFA

Each syllable will take you to a final state from which you must start another syllable.

So what is a syllable? Note that $[$N$]$ means optional N

vowel $[$N$]$ e$.$g$.$ A$,$ AN

d$,$w$,$z$,$y$,$j vowel $[$N$]$ e$.$g$.$ DA$,$ DAN

b$,$h$,$k$,$m$,$n$,$r$,$g$,$p $[$Y$]$ vowel $[$N$]$ e$.$g$.$ BA$,$ BYA, BAN, BYAN

t vowel $[$N$]$ e$.$g$.$ TA$,$ TAN

t s vowel $[$N$]$ e$.$g$.$ TSU, TSUN

s vowel $[$N$]$ e$.$g$.$ SA$,$ SAN

s h vowel $[$N$]$ e$.$g$.$ SHA, SHAN

c h vowel $[$N$]$ e$.$g$.$ CHA, CHAN

I think you will have to have three final states. One is q$0$ and the others are new states.

Make sure every one of the above syllables will go to a final state.