No you cannot. There are only two places in Johto to get the Shiny Stone. While both might be before Olivine City, there is something that prevents you from obtaining the Shiny Stone.
The three ways of getting a Shiny Stone in Johto (there is also a way one in Kanto but that is of no concern here. Also, I know I said two places but one place has two ways of getting a Shiny Stone) is from getting first prize in the Bug Catching Contest, getting it in the National Park, or buying one in the Pokeathlon. However, for the first and third method this can only happen after you obtain the National Dex. Prior to this, you win a Sun Stone from the Bug Catching Contest and just flat out cannot buy a Shiny Stone in the Pokeathlon. As for the second method, you need Rock Climb in order to do this.