Tamron 28-300mm Model 185D Auto Zoom on Nikon d40

Autofocus function on the D40 only supports lenses with the
AF-S feature, which have an autofocus motor built into the lens,
instead of using an autofocus motor drive built into the camera.

The Tamron lens you have, does not have a built in motor and
the autofocus function relies on the motor drive in the camera.

It will not work with the D40 or D60, but it will work with other
Nikon digital SLRs, such as the D80. Need to get an AF-S
type lens or upgrade to different Nikon digital SLR. Unless
you do this, you will have to manually focus the Tamron lens.

All of the Nikon DX (for digital) series lenses are also AF-S
type, so they will work with the D40, which is designed as
an entry level digital SLR, therefore it is intended primarily
for use with DX lenses, which are typically sold in a kit with
the D40. Most common one is Nikkor 18-55mm DX AF-S.

Other Nikon AF-S lenses made for film cameras (FX type)
will also work with the D40, but these tend to be expensive
professional models. DX series lenses tend to be more
affordable. You might consider the 18-200mm DX AF-S
as an alternative to the Tamron, but these are not cheap.