Have House Cannith do it
There are no RAW as far as I could find, so everything listed below is up to your DM, but here is my interpretation based on the Eberron setting and the currently released material for Eberron.
In Eberron, almost all constructs and such are made by house Cannith or one of their licensed workshops. So if you have a broken automaton it would be logical to go to he nearest house workshop/enclave and inquire about repair services.
The fact that you also need to reset its programming only enforces this need to find an expert, as simply fixing all the broken parts would mean you would get the same ingrained enemy as you already defeated.
Determining cost is hard, and can be up to the DM, but I would suggest that the House requests a service instead of gold. This could be anything from looking for rare materials needed for the repairs to a job Cannith needs doing that they see as equivalently valuable.
If you want to do it yourself, or avoid House Cannith, you could try some tinkering tool checks to fix it and at least one very hard check to fix its programming. You could instead find an independent Artificer and hope he/she has the skills for the job.