Good Day,
The oil could be anywhere between an ISO 22 and an ISO 68 but it depends on the design and specifics of the application. I am going to assume that you are considering an oil cooler to minimise the circulating oil's temperature and hence give a similar viscosity across the changing temperature variations. One thing to remember is that the flow was origionally determined by the oils ability to adheer to the ring and this was in part a function of the tackiness or adhesion or surface plating charastics of the oil. These functions are partially independant of ISO viscosity. Also the oil rings supplied the minimum amount of oil required. As long as the oil doesn't cause an imbalance or an oil whirl or oil whip situation you can't put too much oil into the bearing by simple splash methoid. So the more you put in the easier it would be to remove the heat. etc.
Your best bet is still to contact the OEM who has a better understanding of the specific system than the rest of us. Chances are they might have a retro-fit system to sell you. Or they would assist you in designing a system, their reputation is also at risk here.
hope this helps...