Sony A37 has a Sony/Minolta Alpha lens mount and currently there are 143 native lenses available for this mount.
The latest released lenses that are compatible with the A37 are the Lensbaby Sol 45 DSLR, the Venus 105mm F2 and the Lensbaby Burnside 35.
A37 also has a sensor based image stabilization system which means that all of these lenses will be stabilized when used on the A37.
Since Sony A37 has a APS-C sensor, it has a focal length multiplier of 1.5× so you have to multiply lenses original focal length with this multiplier to find the Full Frame equivalent focal length of the lens when mounted on A37.
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Sony A37 Lenses with Image Stabilization
Sony A37 Lenses with Weather Sealings