Parts should not be difficult to get for this forklift truck. The thing that makes it more difficult than the age is the fact that it is an Allis Chalmers. They were not that popular in the day.
Most common wear items should be available aftermarket and any more expensive, larger items should be available used.
Like most other dealers we source parts for most trucks, especially older units, by the type of part. For example, we have a supplier for water pumps, one for starters and alternators, one for hydraulics and so on. I just sold a guy a rebuilt water pump for a 1952 Baker forklift 2 weeks ago.
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