SOFTENING OUTLINES

Now that your sprite is almost looking like the finished product, one problem may remain - those dark, monotone outlines that we started with.

In some parts they are fine, but in others, especially areas where colours are primarily pale, they appear harsh and innapropriate. The obvious solution is to lighten them up a bit.
I'll split this down into three sections:

SOFTENING OUTLINES

In most cases the most appropriate action is to replace the black outline with a colour somewhat closer to its surrounding shades.
Light is an important consideration here. Lines under direct light should be lightened more. Lines in shadow should be lightened less, if at all.
Take the extreme case of this mummy - before and after its outlines have been lightened.

If you want to do this really seriously, you might also want to gradiate lightened lines, using even more shades between their lightest tone and the original black. This ball example shows the basic principle.:


BRIGHTENING OUTLINES

Sometimes the shade you want to replace the lineart with is lighter than line 'and' its surrounding shades. I find this useful along the non-outline edges of a shape where edges meet.
This simple box example says it better :


REMOVING OUTLINES

In some cases the sprite will look better if certain outlines are removed entirely, and replaced by an adjacent colour. This includes instances such as edges between flesh and clothes, and colours painted on a surface.
Take this example of a shirt sleeve hanging on an arm - before and after.