Recharging alkalines will never be more than an interesting experiment. You can buy rechargeable 9V batteries.
Yes, looks like there are some good ones now (LSD NiMH or Li-ion):
http://www.metaefficient.com/rechargeable-batteries/rechargeable-lithium-batteries-9v.html
Good info ...
The Li-ion batteries would seem the most interesting given the greater capacity, but the operating voltage topping off at about 8.4V and running down to about 6V might be an issue. About what voltage will a typical Fluke DMM shutoff? To be more specific, at what voltage will a Fluke 27 (30 years old) and a Fluke 85 (25 years old) shutoff or fail to operate correctly? If the shutoff point or the point where operating is out of spec is, say, 7.5V then you might only get half or less usable capacity. OTH, even at half capacity they should still last longer than the NiMH versions as they too might shutoff before reaching minimum cell/pack voltage.
What would be interesting is the possibility of a single cell Li-ion battery with integrated boost converter to provide 9V all the way down to cell shutoff at 3.2Vish and for the converter to shutoff at that point to protect the cell. I would think the loss of package volume necessitated by the inclusion of the boost converter would be somewhat offset by being able to run a single cell.
Of course, such a device to be practical would obviously have very limited current/power output capabilities, but that might not be a problem for a DMM. Given a nominal 4.4WHr capacity of an alkaline 9V battery and a 1000 hour operating time of a typical DMM the average power requirement is on the order of 4.4mW though it's likely that would be higher when the DMM is sourcing current as it would doing resistance or capacitance measurements. But, a very high frequency boost converter with a power limit of, say, 12mW, might be small enough to be built into the 9V can. Or, the 9V battery clip might have the boost converter and the whole volume of the 9V can could be filled with Li-ion chemicals.
Brian