I need help in designing an opamp circuit with the following features:
A difference of 45.9mV for the Vin will result in a 0.1V difference for the Vout.

For example, if Vin=4.1V and Vout =5V
a change in Vin = 4.05V will make Vout = 4.9V

It doesn't matter what are the values of Vin and Vout, it's the difference that's important.

The way I understand his post is that he wants a unity gain amplifier with a built-in 100mV offset. To do so, you could configure a unity gain amplifier that has a resistor in the feedback, then build a current source that pulls a fixed current through that resistor. In that way, the feedback voltage will always be offset from the output voltage by a fixed amount, and so the output would have a fixed offset from the input.

-Ken