I don't think the KeiTama can connect to any cell phone through infrared. I believe it connects in the same way the Connection-series Tamagotchis connect to the TamaTown / MusicCity web sites - by passwords.
I'm not sure the KeiTama actually connects to a web site either. As far as I can tell from the instruction manual (page 20), it connects to an application called "Tamagotchi Park" that you have to download and run on your cell phone. I'm fairly certain this app runs only on Japanese-language cell phones.
The code in the parents menu is a Tamagotchi Park login password to have your current character visit (or send a message to?) their parent. (Your previous generation.) The corresponding Tamagotchi Part logout password rewards your character with some Gotchi Points. (I believe the amount received is somewhat random.) You can get Gotchi Points from the parents three times.
Here are some logout passwords.
Furawatchi: 12131 31631, 82182 20331, 32133 31231
Mametchi: 31090 25112, 04962 11805, 63083 11091
Memetchi: 21251 54112, 53132 38551, 62113 13351
Kuchipatchi: 84011 13213, 25022 12510, 64063 12714
Debatchi: 65151 11211, 48321 21201, 53153 07811
Dorotchi: 48034 01181, 07113 04213, 64433 12511
Gozarutchi: 33181 11581, 43172 14781, 30681 76135
Kurokotchi: 21221 44118, 20721 04129, 18112 61381
Urutchi: 26115 17173, 22112 18171, 65763 13816
Oyajitchi: 31791 72112, 76117 29205, 63103 15191
Paparatchi: 57110 36195, 36113 26262, 23123 38761
Ojitchi: 52271 12301, 83222 39801, 01102 18137
Otokitchi: 12271 21411, 20612 62122, 66120 01378
How to use the above passwords.
1. Ativate the connect icon (upper right corner of your KeiTama's screen.)
2. At the first screen, select "Ke-tai". It's the bottom menu entry.
3. At the second screen, select "Yuubin". It's the top menu entry, and is next to an icon representing a Japanese post box.
4. At the third screen, select "pasuwa-do". It's the top menu entry.
5. Enter the 10-digit password corresponding to the character type of your previous generation. (For example, if your current caracter is Kuchipatchi, and his parent was Mametchi. You need to use the Mametchi passwords above.) Use the three passwords in the order list above. (from left to right) Press the B (middle) button when you're finished entering a password.
6. (It's been several years since I last ran a KeiTama, so this part is fuzzy.) If, after entering the password, another menu screen appears, with two entries, select the top one.
h34r: UYY40 
