First, you want to use
model <- lm(Total ~ Coupon, data=df)
not model <-lm(df$Total ~ df$Coupon, data=df).
Second, by saying lm(Total ~ Coupon), you are fitting a model that uses Total as the response variable, with Coupon as the predictor. That is, your model is of the form Total = a + b*Coupon, with a and b the coefficients to be estimated. Note that the response goes on the left side of the ~, and the predictor(s) on the right.
Because of this, when you ask R to give you predicted values for the model, you have to provide a set of new predictor values, ie new values of Coupon, not Total.
Third, judging by your specification of newdata, it looks like you're actually after a model to fit Coupon as a function of Total, not the other way around. To do this:
model <- lm(Coupon ~ Total, data=df)
new.df <- data.frame(Total=c(79037022, 83100656, 104299800))
predict(model, new.df)