I realise this is an old thread & I don't know whether you found a solution, but may I suggest you use murasame's suggestion about using Toast. Toast versions 5 (OS 9 & X) & 6 do recognise the m4a format, what's-more it will recognise external burners. Open Toast & click open the Audio tab/window. Drop your m4a files in & Toast will convert them. Then put your blank CD in & press Record (burn.)
It is NOT a good idea to convert mp3 to m4a or vice versa! Both are 'Lossy' formats which means they throw away information to help them compress in size. To compress them twice would have a significant effect upon their quality & most likely quite noticeable. However, converting them upwards to a full audio CD will not result in any loss of quality! Take murasame's suggestion about how to obtain Toast. (I've seen plenty myself.)
In the past & still many cases now, software that accompanies burners is for pc windows only.