My Rogue Trader player wants to start a colony. looking through the colony size changes 90 days seems very rapid , especially as it takes ~120 days to get to the colony site in the first place so in play it would be almost impossible to keep up with the needs for growth, how are other GM's handling this?

I'm leaning towards allowing as part of the initial colony setup (with added objectives etc) the rogue trader to supply/arrange for a number of hard infrastructure upgrades which would mean that for the first however many size increases the colony would count as gaining the upgrade, any upgrades provided as extra would only provide the bonus to the colony once they were actually needed ( so no loading the colony with a dozen of each and gaining very high levels from the bonuses.)

does this sound like a reasonable idea?

The 90-day cycle for Colonies is far too rapid for my game. Not only does it cause the colony to grow unrealistically, it also doesn't allow the players to interact with their colony often enough. I have switched to a year cycle, and reduced the resource depletion to 1d5-2 (minor)/1d5 (major) per year. This has worked well to allow the colonies to grow in a more belivable way. As for resource harvesting for PF, the players are limted to doing to during a year they have visited, and they are still required to convince the colony that it is in their best interests. I generally allow it once per 5 years without forcing the players to risk problems with the colony. If they want to do it more often, they need to roleplay convincing the colony and pass some social challenges.

As for Endeavors for upgrading the colony, my players often make purchases of things the colony will need for its next upgrades and leave them at the colony or have a secondary ship transport them there. Per the book, your colony leader can perform background endeavors for you (with a bonus) and you can buy things you need at the colony with a +5PF bonus as well. If the colony leader needs particular resources for a scheduled upgrade before the players visit, he attempts to purchase it. This purchase counts against the groups aquisitions, and is limited to once per session. So, as the colony grows and time passes the colony leader runs background endeavors as set out by the Rogue Trader. I use the base time of 1 year per endeavor, modified by the background endeavor rules in Into the Storm. So far, it seems to work pretty well and the players are glad to come back and see their colony growing as they intended.