The early 1900s Oliver typewriters do not use the standard half-inch ribbon, but were built to take 7/16" ribbon on a wooden spool-core.
This machine as found had an ill-fitting standard ribbon (crumpling as it passes through the vibrator) and plastic spools that look out of place (and didn't fit the take-up pin).
Since the 1930s replacement spools and ribbon for Olivers have probably been rather hard to come by. However, enabled by the internet's global online-market, today these are again available. Amazingly, it is possible today not only to buy new, inked 7/16" ribbon, but even to obtain a correct ribbon with a new Oliver-type wooden spool-core.
If this machine had been in good condition, this is definitely what i'd have gotten for it. As it is, the ancient Oliver looks a bit of a wreck - splashing-out on new spools seemed 'too much of an honour' for it. More in keeping with the much mucked-about machine, decided to continue 'mucking about' by making some spools and a ribbon at the kitchen table.
Ingredients are a wooden bobbin from the craft-store, veneer salvaged from a French-cheese-packaging, 10mm satin-weave ribbon from the haberdashers and oil-based metal-stamp ink from an online store. Not in the group-picture is one extra hairpin clip, for making the spool-clip.
The Oliver wooden spool-core needs to fit over a capstan with ~5mm spindle and have a recess to fit over the ~16mm diameter spindle-base. Total height of the spool around 11mm. The central section of this bobbin was 18mm, with a 7mm diameter hole. That nicely gives some play and makes dimensioning less critical, so the bobbin was sawed into ~5mm thick 18mm diameter disks and an extra hole for the take-up pin drilled. The veneer was first placed in hot water for a couple of minutes and then wound round a cylinder to dry - this will reduce stress and risk of snapping when gluing as a flange around the wooden disk. With wood-glue, the now-curvy 11mm strips of veneer were wrapped around the disks (held in-place with some rubber-band to give time to completely set).
Held in place with the clips, the ribbon was wound onto a spool. The first few inches were inked by running it over a pad, then the rest of the ribbon was inked by 'painting' the top of the wound ribbon from the bottle. The droplets of ink placed on top of the ribbon are drawn into the fabric.