Mirrorless cameras are by far the best candidates for conversion to Infra Red or Full Spectrum, indeed cameras without Live View, like most DSLR's over about 5 years old are totally unsuitable for Full Spectrum conversions, as the IR filter on the front of the lens will block practically all light to the viewfinder, you won't be able to see or focus at all.
With a mirrorless camera or a camera with live view, you will see on the LCD Panel exactly what the sensor is seeing, so you are seeing infra red light converted to visible light. The other advantage is that the Camera's autofocus system will work accurately because its based on what the sensor is seeing. The problem with a DSLR camera without live view is that the viewing and focusing systems are looking through the lens, but the sensor is seeing something completely different in IR light, the best that can be done is for the viewing system is mis-adjusted to be in focus when the sensor is in focus in IR, but this will only be accurate with the lens it was set up for. Most lenses don't behave consistantly ie. they focus IR light to a different distance to visible light, but as they were not designed for IR, they all need different adjustments. Zoom lenses are not recommended on DSLR conversions, but are fine on Mirrorless camera conversions.
For this reason I can only recommend cameras with live view and because a DSLR's main viewing system, the reflex bit, is virtually redundant, I do Sony, Fuji and Canon Mirrorless Cameras. Mirrorless cameras have evolved over the last few years to be equal in most respects to a DSLR, auto focus speed being an area that has taken a time to improve, but AF speed is rarely a problem with IR photography, so even older mirrorless cameras make good conversions. Where they excel is focus accuracy, as the focusing is done on sensor, so it does't matter what lens or what light is used, the AF system will be equally accurate. [No need for AF Micro Adjustments].
Other advantages of mirrorless cameras are the tend to be small, light, cheap, and they can nearly all take almost any lens with the multitude of adaptors available on the internet. Their live viewing system's normally have some sort of Manual Focus Assist, like MF Magnification or Focus Peaking, which make manual focus easy.
Of the mirrorless cameras on the market the larger sensor APS-C cameras from Canon, Fuji and Sony as well as the Full Frame Sony A7 series cameras are the ideal cameras for conversion, especially those with Electronic Viewfinders such as the Sony Nex 6 [Above Left], Nex 7, a3000, a6000 series and the A7 series. The EVF's make viewing and manual focusing far easier in bright sunlight, which is exactly when IR conditions are best!!
My personal favourites are the Sony A7 series, NEX 6/7 and Fuji X-E1 because of the EVF's, but the Canon EOS M and the NEX 5N/R/T are the best of the more economical options, especially since you can add a very good, but expensive, EVF to the NEX 5N/R/T cameras. You don't even need to be an existing Sony, Fuji or Canon user to use these cameras, partly because you can use almost any lens on them via adaptors, plus it turns out some of the older lenses with less sophisticated coatings actually work better in IR than the latest lenses with their very modern coatings, which seem to cause Hot Spots when the aperture is stopped down. For more about Lenses see the Lenses Tab above.
The Full Frame Sony A7 and A7II series cameras are now available for Full Spectrum Conversion, I have developed a technique to adjust the back focus enough to completely remove the filter stack leaving just the factory sealed sensor coverglass to protect the actual sensor. There is practically nothing between the lens and the actual sensor surface, no Hot Mirror, no IR Filter Pack, no Anti Alias, just the factory coverglass remains. These cameras are the ultimate in IR image quality, the results are simply stunning, especially in Black and White, see the full frame gallery.
Sony Nex 6 590nm Conversion
The Sensor Cleaning mode in all Canon and Sony Cameras is performed by a Piezo Ultrasonic Vibration of the UV/IR Cut Filter which is Florine coated to help the dust drop off when vibrated. Unfortunately this has to be completely removed in both Full Spectrum and IR Conversions, consequently the Sensor Cleaning Mode on all converted cameras is disabled permanently. The Sensor Cleaning Modes were never very effective anyway and without the special Florine Coating there is absolutly no point in reattaching the Piezo Vibration module to the IR filter or full spectrum window [If Fitted]. Just like an unconverted camera normal manual cleaning, initially by a rocket blower is recommended, but careful mechanical dry/wet cleaning can be performed if necessary using swabs or lens pens. Dust spots on an image taken with a Full Spectrum Camera that does not have the un-necessary glass window tend to be easier to remove in Photoshop because they tend to be sharper and smaller because the dust causing the spot is actually on the factory fitted cover glass of thee sensor. However this cover glass is not replaceable, so it should be treated with extra care when cleaning a full spectrum camera.
The sensor cleaning mode in the Sony A7II and A7RII remains operable after conversion as these cameras use the In Body Image Stabilisation [IBIS] mechanism to shake the whole sensor module. I'm not sure how effective the system is either before or after conversion, but it is probably better than nothing.