Fill region between two loess-smoothed lines in R with ggplot

A possible solution where the loess smoothed data is grabbed from the plot object and used for the geom_ribbon:

# create plot object with loess regression lines
g1 <- ggplot(df) + 
  stat_smooth(aes(x = x, y = ymin, colour = "min"), method = "loess", se = FALSE) +
  stat_smooth(aes(x = x, y = ymax, colour = "max"), method = "loess", se = FALSE)
g1

# build plot object for rendering 
gg1 <- ggplot_build(g1)

# extract data for the loess lines from the 'data' slot
df2 <- data.frame(x = gg1$data[[1]]$x,
                  ymin = gg1$data[[1]]$y,
                  ymax = gg1$data[[2]]$y) 

# use the loess data to add the 'ribbon' to plot 
g1 +
  geom_ribbon(data = df2, aes(x = x, ymin = ymin, ymax = ymax),
              fill = "grey", alpha = 0.4)