The 3906 is the a single stack magazine version of the 5906. They were discontinued in 1990. Smith & Wesson should have a stock of parts for it if you need to get it repaired. The 3906 uses many of the same parts as the S&W 3904 (alloy frame blued) and 909 (budget version of the 3904). If you find aftermarket grips, make sure it's for the S&W 390x and not the 391x. 909 grips should work as well. The 391x a compact 3rd generation 39 series; it has a shorter grip and one or two less rounds in the magazine depending on what flavor magazine you get. The plastic base plates have an 8 round capacity, steel 7.
Pachmayr made aftermarket grips for them. Uncle Mike's probably did at one time as well. Hogue has grips for the S&W 39 and 639 which are the 1st and 2nd generation pistols. They may work with your 3906. I would contact them to be sure if they have what you're looking for. The 3904 and 3906 are the 3rd generation.