When I play Gentle Gemdragon, can I ready two of the runes I already used to play him?

Yes, you can.

When you play Gentle Gemdragon, his ability ("When you play me...") triggers and enters the chain. Because this is a triggered ability, you have the opportunity to react to it before it resolves.

Here is the correct sequence:

1. Play Gentle Gemdragon: You pay the energy costs for the unit. This typically involves exhausting runes to add energy to your pool.
2. Trigger: Once he enters play, his ability "When you play me..." is placed on the chain as a pending item.
3. Priority/Reaction: Before that ability resolves, you hold priority. Because Basic Runes have a [Reaction] ability to "Add [1]" (Rule 163.2.a), you can exhaust any remaining ready runes you control to add more energy to your pool.
4. Resolution: The Gentle Gemdragon trigger resolves. You choose up to 2 of your exhausted runes (including the ones you just exhausted to pay for him or add extra energy) and ready them.

According to Rule 415.3.b, players may ready game objects when effects (like the one on Gentle Gemdragon) instruct them to do so. Since your runes are on the board, they are valid targets for this effect.