When discussing openings it is often helpful to give the moves as the names tend to vary. For example, I don't know what the Morphy gambit is. Are you talking about 1. e4 d5? Which is more often called Scandinavian or Center Counter or about something entirely different?
question on Morphy Gambit

so it is:
1.ef e5
2.bc4 nf6
3. nf3 nxe4
4. nc3 nxc3
5. dxnc3 f6
idea keeping black from castling or if black does not f6 then creates interesting possibilities for white to attack f7. However, I was not sure how best to place this if black responds on 1...d5 instead of 1....e5.
Thanks

That would be a different opening, and you can't play 2. Bc4. The usual response is 2. exd5 Qxd5 3. Nc3. Are you asking how to transpose into the Morphy Gambit you've given if black plays 1...d5 instead of 1...e5?
The answer, I guess would be that you can't. If 2. exd5, then there's no pawn on e4 to gambit, to lure the f6 knight away. If 2. e5, then the pawn on d5 blocks Bc4 and you can't then attack f7 in the same way, and the e and d files are still closed.

In the sequence you give we have the Bishops opening/Vienna Game with a bad third move by white. 3. Nc3 makes more sense.
I have been studying this opening, but was wondering what would be white's response to black playing d5 right away to white's e4?
Thanks!