I doubt that the cipher list is documented anywhere. The easiest way to find them is by running Wireshark and see what cipher suites are negotiated.
If you use roUrlTransfer to connect to a secure server, you'll see a set of 31 ciphers available.
However, if you connect to a secure server using any of the UI components (roVideoScreen, etc.), then the only cipher suite supported appears to be TLS_RSA_WITH_AES_128_CBC_SHA. I think this is a bug. It's been reported several times in these forums with no response from Roku.
Here's a Wireshark trace using roUrlTransfer:
Secure Sockets Layer
TLSv1.2 Record Layer: Handshake Protocol: Client Hello
Content Type: Handshake (22)
Version: TLS 1.0 (0x0301)
Length: 163
Handshake Protocol: Client Hello
Handshake Type: Client Hello (1)
Length: 159
Version: TLS 1.2 (0x0303)
Random
GMT Unix Time: Nov 16, 2066 16:48:48.000000000 Pacific Standard Time
Random Bytes: 1c2e904748f6f741e838bea7bbfc1cb8f69a8b532076f917...
Session ID Length: 0
Cipher Suites Length: 64
Cipher Suites (32 suites)
Cipher Suite: TLS_DHE_DSS_WITH_AES_256_GCM_SHA384 (0x00a3)
Cipher Suite: TLS_DHE_RSA_WITH_AES_256_GCM_SHA384 (0x009f)
Cipher Suite: TLS_DHE_RSA_WITH_AES_256_CBC_SHA256 (0x006b)
Cipher Suite: TLS_DHE_DSS_WITH_AES_256_CBC_SHA256 (0x006a)
Cipher Suite: TLS_DHE_RSA_WITH_AES_256_CBC_SHA (0x0039)
Cipher Suite: TLS_DHE_DSS_WITH_AES_256_CBC_SHA (0x0038)
Cipher Suite: TLS_DHE_RSA_WITH_CAMELLIA_256_CBC_SHA (0x0088)
Cipher Suite: TLS_DHE_DSS_WITH_CAMELLIA_256_CBC_SHA (0x0087)
Cipher Suite: TLS_RSA_WITH_AES_256_GCM_SHA384 (0x009d)
Cipher Suite: TLS_RSA_WITH_AES_256_CBC_SHA256 (0x003d)
Cipher Suite: TLS_RSA_WITH_AES_256_CBC_SHA (0x0035)
Cipher Suite: TLS_RSA_WITH_CAMELLIA_256_CBC_SHA (0x0084)
Cipher Suite: TLS_DHE_DSS_WITH_AES_128_GCM_SHA256 (0x00a2)
Cipher Suite: TLS_DHE_RSA_WITH_AES_128_GCM_SHA256 (0x009e)
Cipher Suite: TLS_DHE_RSA_WITH_AES_128_CBC_SHA256 (0x0067)
Cipher Suite: TLS_DHE_DSS_WITH_AES_128_CBC_SHA256 (0x0040)
Cipher Suite: TLS_DHE_RSA_WITH_AES_128_CBC_SHA (0x0033)
Cipher Suite: TLS_DHE_DSS_WITH_AES_128_CBC_SHA (0x0032)
Cipher Suite: TLS_DHE_RSA_WITH_SEED_CBC_SHA (0x009a)
Cipher Suite: TLS_DHE_DSS_WITH_SEED_CBC_SHA (0x0099)
Cipher Suite: TLS_DHE_RSA_WITH_CAMELLIA_128_CBC_SHA (0x0045)
Cipher Suite: TLS_DHE_DSS_WITH_CAMELLIA_128_CBC_SHA (0x0044)
Cipher Suite: TLS_RSA_WITH_AES_128_GCM_SHA256 (0x009c)
Cipher Suite: TLS_RSA_WITH_AES_128_CBC_SHA256 (0x003c)
Cipher Suite: TLS_RSA_WITH_AES_128_CBC_SHA (0x002f)
Cipher Suite: TLS_RSA_WITH_SEED_CBC_SHA (0x0096)
Cipher Suite: TLS_RSA_WITH_CAMELLIA_128_CBC_SHA (0x0041)
Cipher Suite: TLS_RSA_WITH_RC4_128_SHA (0x0005)
Cipher Suite: TLS_DHE_RSA_WITH_3DES_EDE_CBC_SHA (0x0016)
Cipher Suite: TLS_DHE_DSS_WITH_3DES_EDE_CBC_SHA (0x0013)
Cipher Suite: TLS_RSA_WITH_3DES_EDE_CBC_SHA (0x000a)
Cipher Suite: TLS_EMPTY_RENEGOTIATION_INFO_SCSV (0x00ff)
Compression Methods Length: 1
Compression Methods (1 method)
Compression Method: null (0)
Extensions Length: 54
Extension: server_name
Type: server_name (0x0000)
Length: 19
Server Name Indication extension
Server Name list length: 17
Server Name Type: host_name (0)
Server Name length: 14
Server Name: www.google.com
Extension: signature_algorithms
Type: signature_algorithms (0x000d)
Length: 22
Signature Hash Algorithms Length: 20
Signature Hash Algorithms (10 algorithms)
Signature Hash Algorithm: 0x0601
Signature Hash Algorithm Hash: SHA512 (6)
Signature Hash Algorithm Signature: RSA (1)
Signature Hash Algorithm: 0x0602
Signature Hash Algorithm Hash: SHA512 (6)
Signature Hash Algorithm Signature: DSA (2)
Signature Hash Algorithm: 0x0501
Signature Hash Algorithm Hash: SHA384 (5)
Signature Hash Algorithm Signature: RSA (1)
Signature Hash Algorithm: 0x0502
Signature Hash Algorithm Hash: SHA384 (5)
Signature Hash Algorithm Signature: DSA (2)
Signature Hash Algorithm: 0x0401
Signature Hash Algorithm Hash: SHA256 (4)
Signature Hash Algorithm Signature: RSA (1)
Signature Hash Algorithm: 0x0402
Signature Hash Algorithm Hash: SHA256 (4)
Signature Hash Algorithm Signature: DSA (2)
Signature Hash Algorithm: 0x0301
Signature Hash Algorithm Hash: SHA224 (3)
Signature Hash Algorithm Signature: RSA (1)
Signature Hash Algorithm: 0x0302
Signature Hash Algorithm Hash: SHA224 (3)
Signature Hash Algorithm Signature: DSA (2)
Signature Hash Algorithm: 0x0201
Signature Hash Algorithm Hash: SHA1 (2)
Signature Hash Algorithm Signature: RSA (1)
Signature Hash Algorithm: 0x0202
Signature Hash Algorithm Hash: SHA1 (2)
Signature Hash Algorithm Signature: DSA (2)
Extension: Heartbeat
Type: Heartbeat (0x000f)
Length: 1
Mode: Peer allowed to send requests (1)
And using roVideoScreen:
Secure Sockets Layer
TLSv1.2 Record Layer: Handshake Protocol: Client Hello
Content Type: Handshake (22)
Version: TLS 1.0 (0x0301)
Length: 84
Handshake Protocol: Client Hello
Handshake Type: Client Hello (1)
Length: 80
Version: TLS 1.2 (0x0303)
Random
GMT Unix Time: May 25, 2030 05:44:52.000000000 Pacific Daylight Time
Random Bytes: 361e5ac9050932d6b0a191150a0abeb22f5fb3d1530d222e...
Session ID Length: 0
Cipher Suites Length: 4
Cipher Suites (2 suites)
Cipher Suite: TLS_RSA_WITH_AES_128_CBC_SHA (0x002f)
Cipher Suite: TLS_EMPTY_RENEGOTIATION_INFO_SCSV (0x00ff)
Compression Methods Length: 1
Compression Methods (1 method)
Compression Method: null (0)
Extensions Length: 35
Extension: SessionTicket TLS
Type: SessionTicket TLS (0x0023)
Length: 0
Data (0 bytes)
Extension: signature_algorithms
Type: signature_algorithms (0x000d)
Length: 22
Signature Hash Algorithms Length: 20
Signature Hash Algorithms (10 algorithms)
Signature Hash Algorithm: 0x0601
Signature Hash Algorithm Hash: SHA512 (6)
Signature Hash Algorithm Signature: RSA (1)
Signature Hash Algorithm: 0x0602
Signature Hash Algorithm Hash: SHA512 (6)
Signature Hash Algorithm Signature: DSA (2)
Signature Hash Algorithm: 0x0501
Signature Hash Algorithm Hash: SHA384 (5)
Signature Hash Algorithm Signature: RSA (1)
Signature Hash Algorithm: 0x0502
Signature Hash Algorithm Hash: SHA384 (5)
Signature Hash Algorithm Signature: DSA (2)
Signature Hash Algorithm: 0x0401
Signature Hash Algorithm Hash: SHA256 (4)
Signature Hash Algorithm Signature: RSA (1)
Signature Hash Algorithm: 0x0402
Signature Hash Algorithm Hash: SHA256 (4)
Signature Hash Algorithm Signature: DSA (2)
Signature Hash Algorithm: 0x0301
Signature Hash Algorithm Hash: SHA224 (3)
Signature Hash Algorithm Signature: RSA (1)
Signature Hash Algorithm: 0x0302
Signature Hash Algorithm Hash: SHA224 (3)
Signature Hash Algorithm Signature: DSA (2)
Signature Hash Algorithm: 0x0201
Signature Hash Algorithm Hash: SHA1 (2)
Signature Hash Algorithm Signature: RSA (1)
Signature Hash Algorithm: 0x0202
Signature Hash Algorithm Hash: SHA1 (2)
Signature Hash Algorithm Signature: DSA (2)
Extension: Heartbeat
Type: Heartbeat (0x000f)
Length: 1
Mode: Peer allowed to send requests (1)