If it were my power supply, I'd have one that can handle dead shorts with some sort current limiting, and not worry about it. This is inefficient, as power will be dissipated within the power supply.
If you're worried about inrush current harming the supply, put an inductor in series with the capacitor. Inductors resist changes in current, but eventually settle into acting like straight wire. You'll want something like shown here http://www.hammondmfg.com/153.htm with the laminated core and metal mounting bracket.
What size? To get a rough idea... The fundamental equation for inductors is dI/dt = V/L. rearrange this for dI = (V/L)dt and imagine capital Greek deltas instead of the infinitesimal lower case 'd's. The change in current is from zero to the initial inrush current. Let's put dt at 1 sec, since, although we're not trying to build a resonant circuit, the characteristic frequency for a circuit with 1F and 1H is 1 radians/sec. Suppose you get a nice hefty 1H coil. The initial voltage drop across the inductor is 5V. So we get 5 amps. In real life, the ESR of the capacitor and the internal resistance of the power supply, as well as its ability to deliver only so much current, means you probably wont' get that. To limit the current to say 1A means a 5H coil.
The least efficient way to limit current is with a resistor, or a current regulator such as an LM317. But this is likely much cheaper than a 5H coil, unless you already have a coil like that in a junk parts box (these were common in old 1960s/1970s TVs)
Supercapacitor charging circuits can get pretty involved for applications that harvest small amounts of energy, where not one microwatt should be wasted, where >90% efficiency in charging is vital. In some applications, the charging current might be only a small factor greater than leakage current. A good read with technical details: http://www.energyharvestingjournal.com/articles/using-a-supercapacitor-to-manage-your-power-00001921.asp