Ok, then a simple 8 cell battery pack can be made up using a couple of battery holders and a home made connector assembly. On ebay, you will find the type of battery packs originally used in the Alkaline backup setup. Here is a link to some of that type.
http://www.ebay.com/itm/2-Battery-Holders-4AA-Batteries-10-to-12v-DC-Garrett-GTA-350-GTP-1350-GTAx-550-/130839519133?pt=US_Metal_Detector_Accessories&hash=item1e76a49f9d
Next we will need a couple of 9V wired connectors and finally a proper sized dc connector. Wire the two connectors in series so when the two 4 packs of batteries are installed and attached to the connectors, the batteries are in series. Wire all this to the proper size DC plug and you have a backup where you can use Alkalines.
If the battery pack you have for your detector fits in the case, you can either build one like it or go to some place such as batteries plus and show them what you need. I would recommend taking the detector also. They should be able to build you a pack. Personally, I would use NiMh batteries rather than the older NiCads.
Now, they do make a Li Ion AA size and only three of them in a 3 battery holder should work. Unfortunately, I have never found any of that size batteries that were worth the effort. Keep in mind this battery is a nominal 3.7v and not the usual 1.5V. That is why only 3 are needed. Since a VLF doesn't draw much current, they might work out ok. Li Ion batteries are temperamental and never should be discharged fully because it can destroy them. The minimum and maximum voltage is critical. Personally I wouldn't let that voltage get below 3 V per cell or greater than 4.2V per cell. Li Ion's require a special charger to assure the voltages are kept within range when charging.
Reg