Traditional 1:1, 4:1, 9:1 baluns work by connecting currents in series on one side of the device and in parallel on the other side. For a 4:1 balun, voltage is cut in half AND current is doubled to get 4:1 ratio. The following are two suggestions on how to get another ratio that doesn't have an integer square root.
1) For low frequency broadband circuits, simply use a transformer to do both the impedance transformation and to isolate ground for the balanced side. If this is for a low power circuit, check www.minicircuits.com
2) For a fairly narrow frequency range, try using a combination of a 2:1 quarter wavelength transmission line transformer and a 1:1 current balun. Assuming you are trying to connect 50-ohm coax to a 100-ohm balanced antenna, you could use a quarter wavelength long section of 75-ohm coax to get close to a 2:1 impedance ratio along with winding the coax into a coil near the antenna to increase the inductance of the outer surface of the coax shield. Check the ARRL Handbook to get a starting point for coil size and number of turns. For UHF, I make balun coils out of .085in semirigid cable formed into a space-wound coil. Large ferrite beads could also be used to block current flow on the outer surface of the coax. See www.fair-rite.com
for more ferrite information. The end goal of the balun in this case is to prevent the RF current flowing on the inside surface of the coax shield from flowing on the outside surface of the coax shield. You are trying to make the current path on the outside of the coax be a much higher impedance (large inductive reactance) than the load.
A general observation. Hams often worry too much about impedance matching and antenna dimensions, seeming to view 1:1 VSWR as necessary and antenna dimension at if they were handed down by God. RF Engineers have a more irreverant view. First, a 10dB return loss, about 1.9:1 VSWR, (engineers prefer think in terms of the ratio of forward to reflected power) is a pretty good match for many circuits. A 20dB return loss, 1.22:1 VSWR, is considered to be damn near perfect for most situations. Second, if an antenna is small compared to a wavelength, it can't possibly have a lot of gain. It's going to spray RF all over the place and the primary design consideration is efficiency... not wasting RF power as heat. Many times changing the dimensions and shape so it will provide a reasonably good match to 50-ohm coax is a better solution than external matching circuits. For a dipole antenna, the length can be changed, the ends of the antenna can be bent, and/or the feedpoint can be shifted away from the center to change the impedance without changing the pattern significantly. Just get the high current part of the dipole near it's center high up in the air and make sure nothing gets hot.