I'm writing a song with four part harmony. I'm currently in the key of "f". In the alto line, the d goes flat, then in the next measure, the D-flat remains, but the chord seems to suggest an Amajor chord. Would the D-flat still be notated as such, or should it change to C-sharp?
Technically speaking both are acceptable, and indeed in some ways it might be easier for the alto to keep that Df by seeing it spelled consistently.
But I would strongly recommend spelling the latter pitch Cs, as you've done; good for you! It clarifies the harmonic environment immediately, and it'll be especially clear since this is vocal music, perhaps read in open score format.
But, seriously, good job for thinking about this. Too often composers don't, and it really shows their immaturity!
Edit: Is the final chord in your example D minor? If so, definitely spell it as Cs to make it clear that that pitch is tonicizing D.
In fact, is the same thing happening in the previous measure? If the last chord of measure one is a D minor chord, I'd change that Df to Cs, as well.
Ideally, we need to see the other harmonies. However, it looks to me as if the chord sequence is Bb, Bbm6, Bbm to A, resolving to Dm. In that case, the Db is correct as it's in Bbm, but the same note becomes called C# when it's in the A chord. Written that way, the harmony becomes clear to readers who understand what they're doing. It's good that it's done 'right'-well done! The other day a guitarist told me that the major 3rd of C# is F...
I guess for someone who is used to reading their own line and sort of separating it from the others while singing, the Db may be easier to read. But for those who picture the whole voicing of the harmony, then C# is the one.
You haven't shown us enough context. Is the first chord Dm or Bb? Maybe the first Db would be better as C#. In any case, I'd be very wary of asking a singer to read an augmented interval, Db to E.
Show us the whole page, we can offer better advice.