The question is tricky in a fundamental way.
[...] very high uptime [...] longest continuous runtime
One part lies in the definition of these, partly contradicting, terms as well in what the computer is. Uptime is a term used for high level operating systems - such as a Unix system - but the Voyager systems are embedded computers running their application on bare metal. So the basic definition for uptime is already hard to tie to a core component.
Embedded systems are quite different from general purpose systems by being almost entirely interrupt-driven. One feature of embedded systems is that they routinely restart - restart being in fact the most important non-maskable interrupt. All to increase stability. So of course, some 'working since installed' time can be counted (*1), but it is rather meaningless in sense of computing value, as the systems aren't really running continuously.
Even by settling on some hypothetical overall working time, the result is still a rather meaningless value. After all, any such number would only be useful to compare comparable systems - and the Voyager computers are in no way comparable to any non-embedded systems in operation.
The other part is within the meaning of "uptime" itself. It can be given for various components with different meaning. It could define how long a system has been continuously powered. Or how long an OS has been running unstopped on a machine, or how long an application has run unstopped.
Think for example about an x86 machine running Linux running some large scale application like a database server - or better, a MUD. To a hardware person, the power up time is all that counts, while players would only look at the duration their game world persists. Fun part: neither cares about the OS-uptime. In fact, not even the admin does, as his job is to provide a running MUD, not just hardware or an OS.
The single case that the OS-uptime would matter is only true in a situation where the OS itself is the service provided - to many independent users. Not often nowadays, where everyone got has their own machine using services on remote servers - making one of our most favoured benchmark values rather useless to real life :))
Bottom line: The question sounds cool, but doesn't work out in this case.
Now, if we accept all of this and just settle for some 'working since installed' time, the best candidates might well be some traffic light systems of the early 1970s. :)
*1 - Well, and then it can't, as probe systems are usually don't work full-time, but go into sleep mode as often as possible to save on power.