Practicing more slowly will make them more stable. From there you can speed up, gradually. If you start with speed first, it's difficult to ever achieve stability.
Scales, arpeggios, and Hanon exercises are the time-honored ways to build dexterity and strengthen the weaker fingers that can slow down the entire hand.
A great trick for mastering an extended run (for example, a passage of many even eighth or sixteenth notes in a row) is to temporarily alter the rhythmic values of the notes so that you play the first note very long, the second note very short, and continue to alternate in that long/short pattern. Really exaggerate the difference--the long notes should be quite long and short notes very snappy. Do this several times and then flip it around so the first note is short, the second long, and so on. Practice that several times. Continue to switch between rounds of long/short and short/long.
When you then go back to playing it the normal, even way, you'll be surprised at how much easier, faster, and more accurate it is.