Because the shoe is synthetic, you will probably not yield the results you want with a dye. A leather dye is not going to penetrate the polyester fibers and will only give you some surface staining, which it seems you've already discovered.
My advice would be to skip dye and paint the shoe with either floral spray paints or fabric paint. You might want to sponge it or dab it on rather than brushing, so that it works into the fibers rather than sitting on top of them.
"And we are all told from the moment we open our eyes, that everyone is entitled to his or her opinion. Well, thatís horsepuckey, of course. We are not entitled to our opinions; we are entitled to our informed opinions. Without research, without background, without understanding, itís nothing. Itís just bibble-babble. Itís like a fart in a wind tunnel, folks." --Harlan Ellison