The grease on a coil spring is purely to reduce friction between the spring and the fork leg/stanchion. The choice of grease is non-critical beyond ensuring that it is compatible with the existing grease (or you clean the fork thoroughly to remove the old grease) and that it will not damage the seals. Natural rubber seals can be damaged by petroleum based greases however most fork manufacturers appear happy to use petroleum based calcium greases such as Buzzy's Slick Honey so this does not appear to be of much concern in practice.
The 2006 Marchozzi product manual does not mention or recommend a specific grease type. The closest thing I could find to a recommendation was a 2012 video of a Marchozzi employee rebuilding a fork with a similar design where around 17:40 he uses an amber coloured grease (likely calcium grease) to lubricate the dust seals. While there was no clear shot of the product used and no specific grease type mentioned, the recommendation was to use "lightweight low-friction grease".
Following that recommendation you would be safe using most types of general-purpose grease including castor oil based greases (as they will not degrade rubber seals), silicone or teflon grease (also safe to use with rubber), lithium grease, graphite grease, or calcium grease. Greases designed for high temperature/high pressure situations (such as automotive bearing grease) will not be as effective at lubricating a fork spring under typical use so should be avoided unless that is all that is available.