You can spend eggs from any of your birds to pay the egg cost for playing a new bird. There are no restrictions on which birds' eggs can be used, as long as the eggs are on your player mat.

This is supported by the following rule:

• "Pay the corresponding egg cost (if any) by discarding eggs from any birds on your player mat."
  (Page 6)

There are no additional restrictions mentioned regarding which birds' eggs can be used.

Source: page 6

Source: Core Rulebook (pp. 1, 2, 6, 8)