Sunlight is good but, as you note, it is also variable.

By using a good high CRI ("Color rendering index")source, as James Snell notes, and by doing tests with white balance, you will be able to get results with artificial light that have far better consistency than you can achieve with sunlight, and which are close enough to the best that sunlight can give as to be indistinguishable to most viewers.

As James says, most LED and most fluorescent lighting tends to 'have issues' due to the spectral discontinuities in the light emitted. You can obtain special high CRI fluorescent and LED emitters which have CRIs of 90 or more and which will be suited for your purpose. Even light with CRI in the 80-90 range is often usable with care in white balance adjustment and awareness of the issues involved. Some web searching on "Color rendering index" will give you a good feel to what is involved. Most white LEDs and essentially all fluorescent tubes use "phosphor" which is excited by part of the emitters light at the blue (high energy) end of the spectrum as light at other longer wavelengths. High CRI lights phosphor lights generally use a mix of different phosphors to produce a more even spectral spread.

Use of halogen or tungsten lamps will give a more yellow light than sunlight but will have an essentially continuous spectrum. Note that CRI is usually defined with respect to tungsten light so a high CRI source will have a yellow cast.

By using several light sources you may be able to achieve an excellent result with LED and/or fluorescent sources, but use of a tungsten lamp or lamps is 'easy enough' and liable to produce best results overall if attention is paid to colour balance.

As well as CRI there is the closely linked issue of color temperatures. Rather than even start on these, the references below provide an excellent introduction which will allow you to search for anything else you need from a well informed starting point.

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CRI / Color temperature / What light sources to use and why:

CRI - a good place to start - CRI - Wikipedia

Good 4 part article Color Temperature & Color Rendering Index DeMystified - possibly enough to give an excellent feel for the subject. There are arcane extras which experts will argue for aeons, but you'll be well informed by this.

REDUser discussion onLED versus fluro. Hardly definitive but useful - LED vs. Fluorescent Lighting. and TEXT VERSION - less pretty, may be easier to follow.

OSRAM so potentially "biased" BUT also useful Methods of Achieving High CRI with LEDs

Chromawhite high CRI LEDS - selling a product but extremely informative as they give a CRI value for each of the CRI test targets with a range of their products and tungsten-halogen and metal-halide bulbs - plus two 'other LED products' for good measure.