Gears don't need much. These aren't high speed, they're not gonna sling everything off. You'd be fine to put a few drops of whatever "universal" oil you're putting on everything, be it engine oil (I don't recommend that, it's not what it was, but it's not a horrible thing), hydraulic oil, way oil, whatever. Just a couple of drops on each gear path, with your daily oiling points, and it'll walk around every gear in the path. (I believe you have two gear paths, an "inner' and an "outer" path. OIl will find it's way around a whole path, but not across a compound (double) gear, if that makes sense. Grease would be fine, but high maintenance, needing cleaned off regularly. There are open gear lubes in spray bottles if you want, all over the internet or in local farm stores, bigger hardware stores, etc. Or chain and cable lube is similar and works well.
I like oil for little gears. My "general purpose" oil is an ISO 46, that works well, and stays on way longer than it needs to, as I'm in there on the daily list oiling the gear hubs/axles/whatever they spin on, so it's nothing to 'touch them up' while I'm in there.