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I have replaced many burnt out relays. I disassembled the MicroLogix and found the manufacturer of the relay, I believe it was Omron, and I desoldered and replaced the relay.
I have also done numerous relay replacements in Micrologix units, I have done a couple of 1000's and a couple of 1500 ( base units) now. Had enough sense to get work to get a desoldeing station for it though, Got a reasonable one for $300 that works well and makes changing the relays effortless and it has payed for itself many times over even having done the small number of PLC's it has been used on.
All the relays i have changed so far have been Omron G6D-1A-NP relays. I believe the NP stands for Nickel plated ( contacts). The most commonly available version of these relays seems to be Silver contact version. I doubt this matters all that much though.
One Gotcha though is that some of the ones i have found use 21V VDC coil versions of these relays - not that easy to find. Most however use the normal 24 VDC but it's something to be aware of.
I suspect that it wouldn't really with only a 3V difference matter but it was something i had never seen before.
The only problem i have found overall with changing the relays lies not in actually replacing the relays, it's being able to disassemble the Micrologix without breaking the plastic housing, They go quite brittle with heat and age which means you have to be extra careful dismantling them.