Q:

Is "no... but only..." correct?

Is it right to write

There is no money needed, but only time.

when I am trying to express that money isn't required for a particular thing, only time is required?

A:

The conjunction isn't necessary and introduces awkwardness.  You could simply say:

There is no money needed (or required), only time.  

or

No money is needed/required, only time.

