What information, if any, is there available from the motor rating plate?
I'm guessing the bandsaw is an LB1200F, or maybe there's another designation it goes by wherever you bought it? If it's an LB1200F, all I can find out about the motor is that it's 900 Watts; about 1.2 HP. Cutting speeds are given (on 50 Hz mains) as 6.7 and 13.3 metres/sec. I make that about 1300 and 2600 ft/min. They'll be about 20% higher on 60 Hz mains.
You are going to want to get down to around a tenth of that and preferably a bit less.
There's a pretty good chance the motor is an IEC metric-frame unit, rather than one of the NEMA-frame motors generally used in North America.
I'd be looking to identify the frame size to see what options are open to you simply by changing the motor. Whilst I can't find any details on the motor itself, the screws that hold it on seem to be M6, which suggests either a 71-frame or an 80-frame.
My guess would be an 80-frame as the power ties up quite nicely with a 2-pole 80-frame.
http://www.electricmotorservice.net/iechart.pdf
Brook Crompton list 80-frame motors with different pole counts and power outputs.
http://www.brookcrompton.com/upload/20112E__ISS3_W_Alum_IE2_IE3.pdf
The 2-pole (about 3000 RPM on 50 Hz mains) is rated 1.1 kw, 1.5 HP.
The 4-pole (about 1500 RPm on 50 Hz mains) is rated 0.75 kW, 1 HP.
The 6-pole (about 1000 RPM on 50 Hz mains) is rated 0.55 kW, 0.75 HP.
Almost all (metric) motor manufacturers make motors to the standard power/pole count/frame size combinations. One or two are also making some "compact" motors with frames one size down from the standard for the pole count/power output. These tend not to be ideal for use at low speed with VFDs because the cooling is limited by the frame size and I'd avoid them in this application
I'm about to make some pretty big assumptions here, so you'll need to check the actual motor details very carefully.
Changing the (assumed) 2-pole motor for a 6-pole would reduce the speed range by a factor of 3. The power will be halved, but as the speed will only be one third, so the torque at low speed will be increased by 50%.
This would give speeds of 435 and 870 ft/min at 50 Hz; still too fast, but pretty much any VFD should be able to run the motor down to 10 Hz for speeds of 87 and 175 ft/min.
The VFD should also be able to run the 6-pole motor to 120 Hz for speeds of around 1050 and 2100 ft/min. Above the motor's rated speed, it operates at constant power (torque reduces as the speed increases).
The speed reduction at constant torque will mean that you are stuck with the torque provided by the motor: you won't get the torque multiplication that you'd get by gearing down to a similar speed.
If the design of the bandsaw would let you drill new mounting holes to accept a larger frame-size motor and bore out the drive pulley to accept its larger shaft, you could fit a 4-pole motor on a 90-frame (24mm shaft), perhaps even a 100- or 112-frame (both 28mm shaft).
Going for a larger frame size would open up the possibility of significantly more powerful motors. Also, if you use a "Sensorless Vector" VFD, the low-end speed range can usually be extended downwards. My experience is that motors start to feel "coggy" much below about 10 Hz on a standard V/Hz (or V/F) drive, but that they will run smoothly down to 3 Hz or less on an SV drive.
it's an upright bandsaw with (if I remember correctly) a 1hp motor, it's surprisingly not listed on the body of the motor. It has about 6.5" cutting clearance. I don't think they sell these in the US - here's a pic of about how big it is. 
