But I find that modern day examples of computers that use ones complement rather hard to come across.
I can only think of the Unisys Clearpath here - and even they are Itaniums at hardware level by now.
The C standard is obviously written with one's complement machine in mind; for example, it specifies that a signed integer may hold values -32767 to +32767.
Jup, that way either system of signed integer handling (within 16 bits) will conform.
So what is the reason for the decline in popularity for ones' complement architectures?
It was never really popular in the first place. Even with early computers the large majority did use two's complement due the much simpler handling.
While it is true that a ones' complement implementation can save circuitry due the fact that a subtraction is just an addition with the subtrahend being negated (*1,2), it also adds complexity to (micro) program design and adds pitfalls (*3).
Ones' complement offers advantages in multi-word multiplication and division (*4), as well as for certain mathematical tasks (nearing zero from either side). But it adds complexity to hardware and/or software as every operation crossing zero needs an adjustment.
To a certain degree it's in use today almost everywhere, as the IEEE 754 Floating Point standard is based around signed values including signed zero. So with a positive spin it can be said that modern CPUs use both: The core CPU's handling (read integer) is two's complement, while associated FPUs use the advantages of ones' complement.
*1 - That's why the Pascaline uses nines' complement
*2 - But only if it's not negative zero and so on.
*3 - Like the need to always know if a comparison is meant to be numeric and integer so a correction for +/- 0 is to be applied.
*4 - As no additional step for sign calculations is needed.