There's really not much PBBans can do to ban the offending player. All bans require hard evidence, either via streaming log files or screenshots.
However, there are other ways to ban the guy. For one, try banning all the player names he uses. Names in BF2142 can't be as easily changed as GUIDs and what not. Mainly thanks to EA's user login system, which only allows five soldiers per account. Essentially, they'd have to delete/create a new soldier each time. I'm sure there's a way around it, but at least banning his player name should help.
To ban his player name, use PunkBuster. Enter the following commands in either the BF2CC console or via RCON, or if you manage the PunkBuster files yourself, add it directly to the pbsv.cfg file:
pb_sv_badname 0 MrPink
pb_sv_badname is the command, 0 is the time in which the player is given before being kicked (in your case, it should be zero), and MrPink is the player name. Now PunkBuster will kick anyone with "mrpink" in their name (I believe it's case-INsensitive).
I made a server manager program for BF2142 that has a permanent ban feature. Basically, it bans a player IP, PB GUID, keyhash, clan tag, and their player name. It makes it that much harder for them to join our server. Unfortunately, it's not something I'll be releasing to the public any time soon, so the pb_sv_badname via PunkBuster is your best bet.