I made 16 bit EPROM adapter for Willem EPROM programmer.
  In attachment of this mail is schematic diagram of this adapter.
  For programming 27C1024 have to use 27C010 mode, 
  for programming 27C2048 have to use 27C020 mode and 27C4002 have to use 27C040 
  mode.
  Making new version of programming software you could add these programming modes 
  too and also modes for 27C160, 27C400, 27C800, 27C322 and 27C801.
  
On reading 27C series EPROM, the pin31 of the EPROM chip socket should be 
  logical 1.
  (Some manufacturers chips this pin may be in both 1 or 0 but others only in 
  1) 
  
This add-on adapter is actually made and its working well. 
  Schematics is in pdf format but available also in Protel format.  
 Schematic
 
  Schematic You wrote my adapter not capable to program chips but only read.
  That's not right.
  I made it about year ago and using it quite well for both - programming and 
  reading.
  Working principle of this adapter is very simple. With A0 i'm switching 
  between lower
   and higher byte so if address not changes at first the lower byte being 
  writen and on
  changing A0 the higher byte is being writen. 
  
For example: For programming 27C1024 (16x128k) I choose 27C010 (8x256k the 
  result
  of size is same as 27C1024) mode and dip switches are in same position as for 
  27C010 programming. 
  For programming 27C2048 I use 27C020 mode and for 27C4096 I use 27C040 settings.
  On writing lower byte then these 10k resistors are for holding other 
  8 bits in logical 1 state
  and on writing higher byte these are holding again other 8 bits in logical 1.
  
 My solution doesn't need any dramatic change of program. 
  It can be used with already written sub functions.