You could write a data collector script. This script would connect to your vCenter, using the vSphere API, collect the logs using PropertyCollector object, use a callback to check for tasks/events as they are generated (WaitForUpdatesEx), finally use the Splunk SDK to send those logs to your Splunk Instance. At least that's what I did. I used pyvmomi which is a python wrapper around the vSphere SDK.
The folowing github page has some helpful examples to get you started:
https://github.com/vmware/pyvmomi-community-samples
The following link has an example which shows how to use the Splunk SDK for Python to send data into Splunk:
http://dev.splunk.com/view/python-sdk/SP-CAAAEE6
This may be sub-optimal. I used this approach a couple of years ago. I am not sure if this is the best way to go about it.
-sk
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