According to the OED renumeration / remuneration are interchangeable. So too are the associated verbs - renumerate / remunerate. However, some commentators have strong feelings about renumeration being used with its first-cited meaning (i.e. remuneration, see below) "... to be avoided at all costs is the metathesized form renumeration." (R. W. Burchfield New Fowler's Mod. Eng. Usage (1996) 666/2). Remuneration is much more commonly used than renumeration (https://goo.gl/44GQRa).
Remuneration is first cited c.1400, comes from Middle French (remuneracion) and Latin (remūnerātiō), and means reward, recompense; (now usually) money paid for work or a service; payment, pay.
Continuously since the mid 16th century renumeration / renumerate have been used with the same meaning as remuneration / remunerate.
Since 1596, renumeration has also meant 'the action or an instance of numbering or enumerating again'. This is widely held to be it's primary meaning.
The OED suggests that renumeration with the meaning of remuneration is a variant by metathesis (https://goo.gl/lhMZQh) arising from a folk-etymological association with words in numer-.