  We study Ces\`aro $(C,\delta)$ means for two-variable Jacobi polynomials on
the parabolic biangle $B=\{(x_1,x_2)\in{\mathbb R}^2:0\leq x_1^2\leq x_2\leq
1\}$. Using the product formula derived by Koornwinder & Schwartz for this
polynomial system, the Ces\`aro operator can be interpreted as a convolution
operator. We then show that the Ces\`aro $(C,\delta)$ means of the orthogonal
expansion on the biangle are uniformly bounded if $\delta>\alpha+\beta+1$,
$\alpha-\frac 12\geq\beta\geq 0$. Furthermore, for
$\delta\geq\alpha+2\beta+\frac 32$ the means define positive linear operators.
