I have made a custom board wth an Atmega2560 and an FT4232 USB to serial converter. From my PC I can access all serial ports. However I cannot upload any sketch to the 2560. I have not connected an EEPROM to the FT4232. Who can help?

Custom board? Poor description. Can we see the schematics?
Bootloader is uploaded?

The custom board that I designed contains an Atmega2560 chip which is connected via Channel A of the FT4232 chip to an USB connector. The whole board is working. I have installed the 2650 bootloader through ICSP.
I can upload sketches via an FDI232 board which was connected directly to RX, TX and DTR(via 100nF) capacitor.
Sketches can communicate via the FT4232. If I try to upload sketches via the FT4232 directly I get timeout errors. I tried to make a specific board entry into the board.txt file in which I changed the PID and VID to the values of the FT4232. But this is not working.

Is the DTR line associated with channel A of the FT4232 connected to one side of the 0.1uF cap and the other side to reset, just like the FT232? This is needed to generate the reset pulse so that the chip resets into bootloader. Make sure there is only one 0.1uF cap on reset - the one connected to DTR.

Check with DVM or scope to make sure that the DTR pin is being brought low when the serial port is opened (maybe there's some configuration necessary to enable it for the FT4232?)