One way to do this is to use equations whose functional form makes it impossible to end up with a value that make no economic sense (although I think T-bill rates did briefly go negative in late 2008...).
So instead of a linear function like:
y = c(1)*x + z
You might use a log-linear function like:
log(y) = c(1)*log(x) + z
The latter equation generates positive values for y for all values of x and z.
You could also try repalcing the single equation with two equations like this:
y_raw = c(1)*x + z
y = @recode(y_raw>=0, y_raw, 0)
so that y is forced to be non-negative.
This may cause some problems with finding a solution though because the EViews model solution algorithms assume that the model has equations with continuous derivatives and the @recode function makes the derivatives discontinuous. You can certainly give it a try though.