The original Gaelic surname MacCoinnich sounds something like MacCoinni or MacKenny in English, and in medieval & early modern times the letter 'z' (which does not exist in Gaelic) was pronounced like an 'i' or 'y'.

Earliest recorded versions - which also show different spellings of the given-name Coinneach/Kenneth - some of which come from records written in Latin (in which the given-name is often Latinised, but not the surname)
1466: Alexander Mackennych
1479: Kenyeoth McKenze
1480: Kenyeoch Mackenze
1486: Cayniti Makkenze
1488: Keinoch McKenzie
1489: Kennuti Makkenze
1491: Kainach Mackenzie of Kintail
1491: Kenzocht M’Kenzecht of Kintaill
1492: Canoth Makcanehe
1494: Kenzeoch Make[n]ze of Kyntale
1503c: Johanni McKenzee
1504: Johannis Makkenze
1507: Hectori McKeynze alias Auchinroy
1509: John Makkenze of Keantalle
1527: Johannis McKynze
1528: Johannis Makkynze
1530: Johne Mckinzie of Kintale
1532: John M’Kenich of Kintaill
1543: Johne M’Kenze of Kyntaill
1544: Johne M’Kenze of Kyntaill & Hector M’Kanze of Cuntaloid
1549: Kennocht M’kneze
1551: Kenzeoch M’kenze
1583: Johne M’Kainze of Kintaill
1587: Mackanyie (on "Roll of Landlords") & Clankanye (on "Roll of Clans")
1592: Laird of Makengzie
1629: Sir John McKanyee of Tarbett

Alphabetical List of Documented Spellings:
M'Cingie
M'Kainze 1583
M'Kanze 1544
M'Kenich 1532
M'kenze 1543
M'Kenzecht 1491
M'Kenzie 1549
M'Kingie
M'kneze 1549
M'Canzie 1546-1580
M'Kainze 1546-1580
M'Kanze 1580-1593
M'Keinze 1546-1580
M'Keneze 1546-1580
M'Kennze 1580-1593
M'Kenze 1580-1593
M'Kinnay 1544
M'Quhinze 1502
M'Quhynze 1526
M'Whinnie 1739 
Macaweeney
MacCoinnich
MacConnach
Mackanyie 1587
Macenzie 1804
Mackeinzie 1580-1593
Mackena 1684
MacKenna
MacKenney
Mackennych 1466
Mackensey 1828
Mackenyie 1687
Mackenze 1480
Mackenzie
MacKenzie
MacKinna
MacKinney
MacKinnie
Mackynnay 1546
MacQueenie
MacVennie
MacVinnie
MacWeeny
MacWhinnie
Makcainze 1546-1580
Makcainzeoch 1546-1580
Makcanehe 1492
Makcanze 1546-1580
Makcheinzie 1546-1580
Makengzie 1592
Makenyie
Makkanze 1546-1580
Makkennyth 1546-1580
Makkenze 1486
Makkenzie 1580-1593
Makkingie
Makkingze 1513
Makkinzie 1770
Makkngie 1775
Makkynze 1523
Makquhenzie 1546-1580
Makquhinze 1526
Makquhynze 1526
McCenzie 1669
McChiney 1684
McHingzie 1684
McHinzie 1684
McHunzie 1684
McKanyee 1629
McKanze 1503c.
McKeingzie 1649
McKeinyie 1636
McKeinzie 1629
McKennah 1684
McKenney 1684
McKensey 1742
McKenze 1551
McKenzee 1503c.
McKenzeth 1503c.
McKenzie
McKeynze 1507
McKinse 1768
McKinsey 1731
Mckinge 1779
McKingyie 1680
McKinze 1503c.
McKinzey 1820
Mckinzie 1530
McKinzie 1684
McKinzsay 1775
McKonze 1503c.
McKwhinney 1684
McKynze 1527
McQuhine 1684
McQuhinny 1684
McWhynie 1684