You could get more eggs while changing colors. To change your yoshi's color just get more points.

Blue yoshi (Can hold 35 eggs) - Get 100 points in flying level
Yellow yoshi (Can hold 40 eggs) - Get 120 points in flying level
Red yoshi (Can hold 45 eggs) - Get 140 points in flying level
Black yoshi (can hold 50 eggs) - Get 160 points in flying level
Sky blue yoshi (Can hold 25 eggs) - Get 60 points in the flying level
Pink yoshi (Can hold 30 eggs) - Get 80 points in the flying level