NBA - just finished season, many players, even those that played in the playoffs have made the trip to Toyoko. So seems like the NBA could continue to supply players for the Olympics.
Golf - they could continue to play at the Olympics since an event could easily be scheduled for a Thursday-Sunday as usual.
MLB - no event
NHL - winter event that has supplied players, but it is an issue as the Olympics occur right in the middle of their season.
NFL - no event
Tennis/ATP - super long season normally, could make it a Grand Slam event, or a 1000 event and schedule into season every 4 years. One difficult thing is that doubles teams aren't always from same country. So they would need to mix and therefore affect rankings.
I think it could easily be done for most leagues. The issue is money. The NBA/NHL/PGA/ATP have no immediate financial motivation for sending their players but carry risk in that players can get injured. However, if they see the Olympics as a new source of fans (and therefore income) it could be a win-win.