Is it possible to build OpAmp circuit with "anisotropic" gain?
Best write down what you want:

$$V_{out}(t) = V_{in}(t) \cdot \begin{cases}
k_1 &amp;\text{if}&amp; \frac{\mathrm d V_{in}}{\mathrm d\,t} &lt; 0\\
k_2 &amp;\text{else}
\end{cases}\label1\tag1$$

So, all just standard things you can piece together. Wikipedia even has nearly all these...


Build a inverting differentiator (standard opamp configuration, 1 capacitor, one resistor).
Build a comparator to convert sign to a maximally clear high or low.
use said high or low to activate an analog switch IC, power opamps of the gain you want, bias a PIN diode if you're working with RF,… to select an amplified version with the right gain.



  I was curious if it is possible to make OpAmp circuit with gain that is dependent on sign of dv/dt


Proof by examples: yes, it's possible, but since \$\eqref1\$ is a strongly nonlinear behaviour, it can't work with linear circuitry like capacitors, resistors and opamps alone. You need some nonlinear behaviour. 

The question really is whether you actually want that. Sounds like a bad idea in any application I can think of. Your question is interesting as an electronics project in itself – but I almost guarantee you, whatever it is that you're going to build with it won't be very robust against noise, the output will be spectrally most surprising, and you'll be surprised how little you will actually enjoy the jumps in output voltage that you specified this way.