These games seem to be unpublished. Martins won the match. These games were recorded in a notebook by R. Martins, which is at the Cleveland Public Library. And some of the games were recorded colors reversed, with no other clue which player was Black or White. Perhaps Martins recorded the games with square one on his side, or maybe the other way around.
[Event "World Championship Match 1859"]
[Date "1859"]
[Black "Martins, R."]
[White "Wyllie, J."]
[Result "0-1"]
11-15 23-19 8-11 22-17 4-8 25-22 9-13 17-14 10-17 19-10 7-14 24-20 3-7 27-23 6-10 28-24 1-6
24-19 6-9 31-27 2-6 19-16 12-19 23-16 14-18 22-15 10-19 21-14 9-18 16-12 19-24 12-3 24-31
3-1 31-22 1-6 11-15 6-10 15-19 10-15 19-23 29-25 0-1
[Event "World Championship Match 1859"]
[Date "1859"]
[Black "Wyllie, J."]
[White "Martins, R."]
[Result "1/2-1/2"]
[Comment "game recorded C.R."]
11-15 23-19 8-11 22-17 9-14 25-22 11-16 24-20 16-23 27-11 7-16 20-11 3-7 28-24 7-16 24-19
16-23 26-19 4-8 30-26 8-11 26-23 5-9 17-13 11-15 32-28 15-24 28-19 10-15 1/2-1/2
[Event "World Championship Match 1859"]
[Date "1859"]
[Black "Wyllie, J."]
[White "Martins, R."]
[Result "1-0"]
[Comment "game recorded C.R., final position is an easy draw"]
11-15 23-19 8-11 22-17 9-14 25-22 11-16 24-20 16-23 27-11 7-16 20-11 3-7 28-24 7-16 24-19
16-23 26-19 4-8 30-26 8-11 26-23 5-9 17-13 10-15 19-10 6-15 13-6 1-10 31-27 12-16 27-24
16-20 32-27 2-6 23-19 11-16 19-12 15-18 1-0
[Event "World Championship Match 1859"]
[Date "1859"]
[Black "Wyllie, J."]
[White "Martins, R."]
[Result "1/2-1/2"]
[Comment "game recorded C.R."]
11-15 23-19 8-11 22-17 9-14 25-22 11-16 24-20 16-23 27-11 7-16 20-11 3-7 28-24 7-16 24-19
16-23 26-19 4-8 30-26 8-11 26-23 5-9 17-13 10-15 19-10 6-15 13-6 1-10 31-27 12-16 29-25
15-19 23-18 14-23 27-18 19-23 22-17 10-15 18-14 23-26 25-22 26-30 17-13 30-25 22-17 25-22
1/2-1/2
[Event "World Championship Match 1859"]
[Date "1859"]
[Black "Martins, R."]
[White "Wyllie, J."]
[Result "1-0"]
11-15 22-18 15-22 25-18 8-11 29-25 10-14 25-22 7-10 24-20 12-16 27-24 4-8 24-19 8-12 32-27
9-13 18-9 5-14 22-18 1-5 18-9 5-14 26-22 13-17 22-13 14-18 23-7 16-32 21-17 3-10 30-25
11-15 25-21 15-18 17-14 10-17 21-14 18-22 14-9 22-25 9-5 25-30 5-1 6-10 13-9 30-25 1-6
10-14 1-0
[Event "World Championship Match 1859"]
[Date "1859"]
[Black "Martins, R."]
[White "Wyllie, J."]
[Result "1/2-1/2"]
11-15 22-18 15-22 25-18 8-11 29-25 10-14 25-22 7-10 24-20 12-16 27-24 4-8 24-19 8-12 32-27
9-13 18-9 5-14 22-18 1-5 18-9 5-14 19-15 11-18 20-11 18-22 26-17 13-22 23-19 22-25 11-8
25-29 8-4 29-25 4-8 25-22 8-11 14-18 11-16 6-9 27-24 18-23 16-11 10-14 11-15 23-27 24-20
27-32 30-26 22-25 26-23 2-7 15-18 7-11 31-27 25-30 18-22 9-13 22-18 30-26 18-9 26-22
1/2-1/2
[Event "World Championship Match 1859"]
[Date "1859"]
[Black "Martins, R."]
[White "Wyllie, J."]
[Result "1/2-1/2"]
11-15 22-18 15-22 25-18 8-11 29-25 10-14 25-22 4-8 24-19 11-16 27-24 16-20 31-27 7-10
19-15 10-19 24-15 6-10 15-6 1-10 23-19 14-23 27-18 8-11 22-17 9-14 18-9 5-14 17-13 2-6
26-22 20-24 22-17 14-18 17-14 10-17 21-14 6-10 14-7 3-10 13-9 10-14 19-15 11-16 28-19
16-23 1/2-1/2
[Event "World Championship Match 1859"]
[Date "1859"]
[Black "Martins, R."]
[White "Wyllie, J."]
[Result "1/2-1/2"]
11-15 22-18 15-22 25-18 8-11 29-25 10-14 25-22 4-8 24-20 12-16 28-24 8-12 24-19 7-10 32-28
9-13 18-9 5-14 22-18 1-5 18-9 5-14 19-15 1/2-1/2
[Event "World Championship Match 1859"]
[Date "1859"]
[Black "Martins, R."]
[White "Wyllie, J."]
[Result "1/2-1/2"]
11-15 22-18 15-22 25-18 8-11 29-25 10-14 25-22 4-8 24-19 11-16 27-24 16-20 32-27 7-10
19-15 10-19 24-15 6-10 15-6 1-10 27-24 20-27 31-24 8-11 24-20 3-7 28-24 9-13 18-9 5-14
22-18 14-17 21-14 10-17 24-19 1/2-1/2
[Event "World Championship Match 1859"]
[Date "1859"]
[Black "Wyllie, J."]
[White "Martins, R."]
[Result "1/2-1/2"]
[Comment "game recorded C.R."]
11-15 24-20 15-18 22-15 10-19 23-16 12-19 27-23 8-12 23-16 12-19 32-27 4-8 27-23 8-12
23-16 12-19 1/2-1/2
[Event "World Championship Match 1859"]
[Date "1859"]
[Black "Martins, R."]
[White "Wyllie, J."]
[Result "1/2-1/2"]
11-15 22-18 15-22 25-18 8-11 29-25 10-14 25-22 7-10 24-19 11-16 27-24 16-20 19-15 20-27
31-24 10-19 24-15 6-10 15-6 1-10 28-24 4-8 24-20 8-11 32-28 1/2-1/2
[Event "World Championship Match 1859"]
[Date "1859"]
[Black "Wyllie, J."]
[White "Martins, R."]
[Result "1/2-1/2"]
[Comment "game recorded C.R."]
11-15 23-19 8-11 22-17 11-16 24-20 16-23 27-11 7-16 20-11 3-7 25-22 7-16 22-18 9-14 18-9
5-14 28-24 4-8 29-25 8-11 26-23 16-20 31-27 11-15 17-13 1-5 13-9 6-13 25-22 2-6 23-18 14-23
27-11 20-27 32-23 12-16 11-7 10-14 7-2 6-9 22-18 16-20 2-6 20-24 30-25 24-27 25-22 27-31
22-17 13-22 6-13 1/2-1/2
[Event "World Championship Match 1859"]
[Date "1859"]
[Black "Wyllie, J."]
[White "Martins, R."]
[Result "1/2-1/2"]
[Comment "game recorded C.R., illegal move"]
11-15 23-19 9-14 22-17 5-9 26-23 9-13 24-20 15-24 28-19 13-22 25-9 6-13 23-18 8-11 29-25
11-16 20-11 7-23 31-26 4-8 26-19 8-11 18-14 10-17 21-14 13-17 1/2-1/2
[Event "World Championship Match 1859"]
[Date "1859"]
[Black "Wyllie, J."]
[White "Martins, R."]
[Result "1/2-1/2"]
[Comment "game recorded C.R., illegal move, one player had a win"]
11-15 23-19 9-14 22-17 5-9 26-23 15-18 17-13 1-5 30-26 8-11 19-15 10-19 24-8 4-11 28-24
12-16 26-22 3-8 22-15 11-18 24-20 8-11 32-28 16-19 23-16 18-22 25-18 14-32 16-12 9-14 12-8
11-16 20-11 7-16 8-3 16-20 3-8 32-27 31-24 20-27 28-24 27-31 24-19 31-26 19-15 14-18 15-11
18-22 8-12 26-23 11-8 23-18 8-3 1/2-1/2
[Event "World Championship Match 1859"]
[Date "1859"]
[Black "Martins, R."]
[White "Wyllie, J."]
[Result "1/2-1/2"]
9-14 22-18 5-9 25-22 11-16 24-19 8-11 22-17 9-13 18-9 13-22 26-17 6-22 30-26 2-6 26-17 6-9
17-14 9-18 23-14 10-17 21-14 16-23 27-18 12-16 32-27 4-8 27-23 8-12 29-25 1/2-1/2
[Event "World Championship Match 1859"]
[Date "1859"]
[Black "Wyllie, J."]
[White "Martins, R."]
[Result "1/2-1/2"]
[Comment "game recorded C.R., illegal moves, strange game"]
11-15 23-19 8-11 22-17 9-14 25-22 11-16 24-20 16-23 27-11 7-16 20-11 3-7 28-24 7-16 17-13
4-8 22-18 14-23 1/2-1/2
[Event "World Championship Match 1859"]
[Date "1859"]
[Black "Martins, R."]
[White "Wyllie, J."]
[Result "1/2-1/2"]
11-15 23-19 8-11 22-17 9-14 25-22 11-16 24-20 15-24 20-11 7-16 27-11 3-7 28-24 7-16 26-23
16-19 24-15 10-26 30-23 4-8 17-10 6-15 23-18 8-11 18-14 11-16 22-17 15-18 14-9 5-14 17-10
18-22 32-28 16-19 21-17 12-16 17-13 19-23 28-24 16-20 24-19 23-27 31-24 20-27 19-16 27-31
16-11 31-26 10-7 26-23 7-3 23-18 13-9 18-14 9-5 14-10 3-8 22-26 8-12 26-30 11-8 10-7 8-4 7-3
4-8 2-7 8-11 7-16 12-19 3-7 19-24 7-11 24-28 11-15 1/2-1/2
[Event "World Championship Match 1859"]
[Date "1859"]
[Black "Martins, R."]
[White "Wyllie, J."]
[Result "1-0"]
11-15 23-19 8-11 22-17 9-14 25-22 11-16 24-20 15-24 20-11 7-16 27-11 3-7 28-24 7-16 26-23
16-19 24-15 10-26 30-23 4-8 17-10 6-15 23-18 8-11 18-14 11-16 22-17 15-18 14-9 5-14 17-10
18-22 32-28 16-19 21-17 12-16 17-13 19-23 28-24 16-20 24-19 23-27 31-24 20-27 19-16 27-31
16-11 31-26 10-7 26-23 7-3 23-18 13-9 18-14 9-5 14-10 3-8 22-26 8-12 26-30 11-8 10-7 8-4 7-3
4-8 2-7 8-4 7-11 4-8 11-16 12-19 3-12 19-24 12-16 24-28 16-19 28-32 19-23 32-28 30-26 28-32
26-31 32-28 31-27 28-32 27-24 32-28 23-19 29-25 24-27 25-21 27-32 21-17 32-27 28-32 27-23
32-28 23-18 28-32 18-22 17-13 1-0