How would you encrypt-then-MAC when using pen-and-paper and a Caesar cipher?
One option would be to get them to select a one-time MAC of the form:

$mac(m,k_0, k_1) = (k_0 \times m + k_1) \mod p$

You would select $p$ to be something like 29. $k_0$ and $k_1$ would be chosen at random from the values 0-29. $k_0$ has the additional restriction that it can't be 0. 

You can aid the computation by giving them a 29x29 matrix of all multiplications mod 29 and a similar table for all additions mod 29.

You'd then work through the message a letter at the time. Suppose these were the letters were numbered: $m_0 \dots m_i$. You'd start at $m_0$, computing the mac equation above. Then you'd feed the mac output in to the $k_1$ position for the next message block:

$mac(m_1, k_0, mac(m_0, k_0, k_1))$

and so on and so on:

$mac(m_i, k_0, mac(m_{i-1}, k_0, \dots))$

The final result is simply the output of the MAC. 

Even though it isn't secure it demonstrates at least the idea of a MAC. It also gives them a design that can be trivially extended in to a secure MAC with small alterations.