I would like to use the timer methods for the NewPing library on an ATTiny841.
In the documentation you mention that the ATTinies do not have "a suitable timer". What do you mean by that ?
As far as I can see you are using a 8-bit timer on the atmega328, and there is an 8 bit timer on the ATTiny84 and ATTiny841 as well.
As I use the ATTiny841, which has two 16 bit timers and one 8 bit timer, I'm a bit confused why it would not be possible to use any of the 16 bit timers ?
Maybe the ATTiny841 is newer than the last time I looked into this or maybe I didn't know about the ATTiny841 or maybe it doesn't have the proper timer addresses. Not sure, nor could I test this as I don't have this chip.
But, did you try it? Looking at the code (line 207 of NewPing.h) it seems that it's specifically looking for known ATtiny microcontrollers that don't have the needed timer addresses to work. The ATtiny841 isn't listed, so the timer would be enabled for the ATtiny841.
In other words... If at the time of writing all ATtiny processors didn't work, then the documentation would say as such. But, if at a later date something was released that did support timers in the needed way, and that microcontroller was not known to me, then the documentation wouldn't updated, as how could it if it's unknown.
Basically, you should try it out and report back if it works.