Are you referring to human or pre-clinical MRI? Desktop preclinical MRI systems have been available for some time now (see the attached link) - these use resistive magnets due to safety and cost considerations.

http://mri.tamu.edu/papers/magma_2002_13%283%29_wright.pdf

In addition to the work from Steven Wright's group listed above here is a list of links to companies or research groups that have developed small scale/desktop MRI systems.  I doubt this list is exhaustive, just what I know off the top of my head.  Within this list all sorts of magnets are used.  Magritek uses the Earth's magnetic field for their Terranova system.  MR Solutions uses cryogen-free superconducting magnets.

https://gate.nmr.mgh.harvard.edu/wiki/Tabletop_MRI/index.php/Main_Page

http://pure-devices.com/

http://www.mrtechnology.co.jp/english/post_474/

http://www.magritek.com/products/benchtop-mri/

http://www.mrsolutions.com/products/imaging-systems/7t-mri/

http://www.bruker.com/products/mr/preclinical-mri/icon/technical-details.html

http://www.winex-instrument.com/nmr.php

Thank you Sir