Is there a Macgyver-esque way to charge rechargeable batteries?

1. Check whether your batteries are NiMh (or NiCd) or Lithium. Don't mix them, as they have different charging and discharging requirements. I assume you're not talking alkalines, and that you know you can't charge them :).

2. Use the 5 V output of the panel, anything higher will risk to blow up your batteries. As it's probably USB, it should be also limited (or it should be possible to limit) to 500 mA, which is actually still pretty high for Lithium batteries, and even more so for Nickel-based batteries.

3. Put at least 3 batteries in series (connecting the plus of one to the minus of another and so forth...). This will sum up their nominal voltage to about 4.5 V. For your safety, use only similar batteries (in capacity and chemistry) and possibly with the same charge level.

4. A resistance, as JoErNanO proposes, can be a good idea to limit the current. However, it won't prevent the batteries from overvoltage, and this can be quite dangerous so every once in a while check their charge level and if it's more than - say - 50-60%, stop charging them and use them. A better limiter for the voltage would be a diode, as it drops an approximately constant voltage. Try to also limit the current to less than 0.5 C, possibly less. 1C means that your battery fully charges in an hour (900 mAh -> 900mA).

You can also refer to the Nickel-metal-hydride guide, and Lithium guide at Battery University, they're quite complete and reliable. There is also a guide for charging from a USB port that should serve your purpose.

Unfortunately you can't really charge batteries without a blocking diode which acts as a one way valve for the electricity. Judging by the fact that you didn't have access to AA batteries, you probably don't have a spare electronics parts store. Did you try asking for mignon or R6s (regional names for AAs)?