A constant current diode is just a JFET with the gate tied directly to the source. If you have a good collection of JFET's, you can likely find one where the I(sub)DSS is 4 mA. There is usually quite a spread in this current so picking a particular JFET should be done based on this spread. For example, the I(sub)DSS of a 2N4416 is typically between 5 and 15 mA. Some common JFET's and their corresponding I(sub)DSS ranges are shown in the table below.
Having used many PCB Piezotronics parts before, I can suggest that you buy their charge amplifier if you need the ultimate in performance. If you can wait a while for mail order, Mouser stocks the 1N5311 diode which is spec'ed to be within the range of 3.24 to 3.96 mA.
Dr. Barry L. Ornitz snipped-for-privacy@live.com
JFET Manufacturer I(sub)DSS Minimum I(sub)DSS Maximum MPF-102 On Semi
2N4416 Vishay 5 mA 15 mA 2N3819 Vishay 2 mA 20 mA MPF-102(obs.) Motorola 2 mA 20 mA 2N5457 Fairchild 1 mA 5 mA 2N5458 Fairchild 2 mA 9 mA 2N5459 Fairchild 4 mA 16 mA PN4303 Fairchild 4 mA 10 mA BFR30 NXP (Philips) 4 mA 10 mA BFR31 NXP 1 mA 5 mA 2SK722E Sanyo 2.5 mA 6 mA MPF-102 Fairchild 2 mA 20 mA 2N5557 Central 2 mA 5 mANote: P-channel or N-channel determines the "direction" of the constant current diode.