The Eton Dorney rowing lake in parkland to the west of London and Greenwich Park, where the equestrian competition will be held, are the two major outdoor venues on sites of environmental significance.
Coe said in the first of a series of daily briefings at the Olympic media centre that months of rain, which may be about to lift according to some forecasts, had posed a problem.
"I spent most of Sunday in the Olympic stadium watching a goodly chunk of our 15,000 volunteer cast heroically rehearsing in the rain," he said.
"I've joked in the past about the challenge of putting a roof across the whole country but this is actually proving quite a challenge to us.
"We've got waterlogged sites, we've got resurfacing that's taking place in some of our areas, particularly some of our more sensitive rural sites," added the double Olympic gold medallist.
Workers are having to lay down a trackway and surfaces for spectators and vehicles, now and during the Games, at the Greenwich venue while extra shelters are also being put in place for venue staff.
Coe said there were long-standing plans, factored into budgets, that could lead to a slippage of the schedule if the worst came to the worst.
"We've got the contingency of extra days available to us in rowing and in equestrian sports, as a last resort of course," he declared. "We've got an alternate sailing course available to us at Weymouth and of course we've got the famous roof at Wimbledon."
He said there was no risk of venues not being ready in time and while there was still work to be done, it was not substantive.
With 10 days to go until the opening ceremony, Coe said preparations were on track.
Some 96 of the 204 countries competing at the Games had checked into the Village on its opening on Monday with 733 of an expected 17,000 athletes and officials in residence by the end of the first day.
Coe addressed concerns about security, saying it had not and would not be compromised by the failure of G4S to mobilise staff.
He also played down reports of first day traffic problems and bus drivers getting lost on the journey from the airport to the Village in east London.
"But for a missed turning and a couple of Tweets, we're in pretty good shape," he smiled.
"I don't think we should get out of proportion some of these issues. We had a tweet yesterday talking about a four-hour delay, it was actually two and a half. We had a driver that missed a turnoff.
"Out of 100 coach journeys that's likely to happen. The majority of athletes got in good shape and on time. Getting in from the airport and to the village is important, and 98 percent of those journeys went without any hitch at all yesterday."