You should Look for an Microcontroller with enough interrupt sources.
An ATtiny2313 has 8 Pin Change Interrupt sources.
The Problem is, the Interrupt will be triggered at any Change of one of the Pins.
At L->H also than at H->L change.
In the Interrupt routine you must find out witch Input Pin the Interupt has triggered and whith change L->H or H->L has occured.
Then you can Count up an Variable for that Source.
Many Controllers oft the AVR Tiny an ATMEGA series offer this Pin Change Interrupts.
INT where useful also and easyer to use, but only the biggest ATMEGA Controllers has more than 3 or 4 of this Interrupt Sources.