Why are Lincoln Roosevelt Jefferson and Washington on US coins and not other presidents?

It was a matter of timing and politics.

Lincoln was the first president to appear on a circulating US coin. His image was chosen because the cent was due for a redesign during the first part of the 20th century which coincided with plans for his Centennial celebration.

Washington was the next of the most-famous presidents whose Centennial was celebrated in 1932. The familiar quarter was supposed to be a one-year commemorative coin but proved to be so popular that Congress made an exception to allow the design to continue.

When the nickel came up for redesign in 1938 it was felt that Jefferson should be similarly honored because he too is considered to be among the greatest presidents.

Roosevelt and Kennedy were put on coins in response to popular sentiment following their deaths while in office.

Eisenhower was picked not only for his role as Supreme Allied Commander during WWII but because he was the most-honored Republican president after Lincoln and both FDR and JFK were Democrats.

Unfortunately each coin has now developed a constituency among its President's supporters and home-state Congressional delegations. That political gridlock has effectively frozen the chances of replacing any of the Presidents currently depicted, despite other worthy candidates such as Theodore Roosevelt or non-presidents like Thomas Edison or Martin Luther King.