Not quite my line of country (I do have a few bus ticket machines) but -
re-inking a ribbon is usually not a good idea, as you'll never get the thin consistency of ink that a ribbon would have - finding an alternative source of new ribbons would probably be better and less messy. Too little ink is going to be a better mistake to make than too much if you do resort to it.
Alternatively, you might get somewhere re-winding the ribbon or it has been out of use for a while, just wind the ribbon on and you may find a bit that hasn't dried out yet.
Are we talking something akin to an
Edmonson ticket dating stamp? Other heritage railways may be in a similar position unless this is something very non-standard.
Would an enquiry via Heritage Railway Association be an option? I'm aware the equivalent for transport / bus museums does a monthly circular for putting people in touch with each other to get supplies, or do bulk purchases and that sort of thing - HRA may do similar.
One thought if you are going to try re-inking something - if the machine you have got has metal / steel moving parts or type, then you do not want to use water based ink, as this will lead to rusting. Stamps Direct (Norwich) are one of the few suppliers I know for oil based inks (link
here) - conversely, oil based ink and rubber stamps are not a good mix.