What accuracy do you need?
Measurements up to Gigaohms is usually a task for Electrometers - maybe you can get a Kethley 610C, these are very useful and don't need expensive cables, since they still use a SO239 connector instead of Triax.
If you can't find one and accuracy requirements aren't too high, an insulation tester could do the job. But these devices work with high voltages (usually up to 1000V)
and still not many go as high as 1 Gohm.
EDIT: seems like either my memory wasn't serving me well or times have changed since I've last looked

Finally there's also the cheap yet accurate and safe method: Get your DMM and measure its input impedance with another (accurate) DMM. It should be close to 10Mohm, but it doesn't really matter if you know the exact value for each of the ranges you're going to use. Put the unknown resistor in series to the meter input and measure e.g. a 10V DC source (could be a function generator or a lab PSU). Then measure the voltage and do the math...

For 10V and 1Gohm and precisely 10Mohm input impedance, you should measure something close to 100mV (99.9mV exactly).
EDIT: especially newer DMMs might not have the very low input current that is required for this. So you should check the accuracy of that method with a known high resistor value beforehand.