How to select series resistor for a Zener Diode
First, you have to consider that every (Zener) diode has a power rating. From this power rating, you can calculate a maximum current for the diode. E.g., if a Zener diode has a maximum power rating of \$ 1~\text{W} \$, and a voltage rating of \$ 2~\text{V} \$, the maximum current through the diode should be \$ 0.5~\text{A} \$. If you want to connect this diode to a voltage supply of \$ 5~\text{V} \$, then you need something (a resistor) that will create a voltage drop of \$ 3~\text{V} \$:

$$ R = \frac{5~\text{V} - 2~\text{V}}{0.5~\text{A}} = 6~\Omega $$

Power rating for this resistor should be at least \$ P_R = I^2 R = 1.5~\text{W} \$.

Now, you want to place some load in parallel to the Zener diode. This will reduce the current through the diode, which will result in a lower voltage. To calculate exact operating point, i.e., voltage drop at the Zener diode, we need more information on this diode, like its \$U\$-\$I\$ static characteristics.

As for the 1N4681 diode datasheet, you can see that its maximum voltage is \$ V_{\max} = 2.52~\text{V} \$, and its minimum voltage is \$ V_{\min} = 2.28~\text{V} \$. The actual operating voltage will depend on the current through the diode, which depends on the series resistor, as well as on the load that is in parallel to the diode. You can also see that the maximum current is \$ I_{\max} = 0.095~\text{A} \$. The maximum voltage would occur for maximum current through the diode. Also take into account that the power rating for \$ 100~\Omega \$ resistor should be at least \$ 1~\text{W} \$.

I've looked through your model - everything is fine except for \$ R_S \$ parameter in the diode. Change this parameter to \$ 0~\Omega \$, and everything will be fine. For this particular diode, you may want to set the series resistor to \$ 80~\Omega \$.



Voltage drop on the Zener diode at the breakdown voltage region can be approximated using a linear function, as follows:

$$ V_D(I_D) = k I_D + c $$

where \$k\$ and \$c\$ are the diode parameters. The voltage equation for the system is as follows:

$$V_S = I R + V_D(-I), \quad I_D = -I ,$$

where \$V_S\$ is the voltage source, \$ I\$ is the system current, and \$ R\$ is the series resistor. Combining these two equations, we get the \$U\$-\$I\$ static characteristics of the system:

$$V_S = I(R-k) + c$$