The MMC2107CFCAG33 went EOL in 2019. The MMC2114CFCAG33 went EOL in 2020.
These products are usually only supported for development and programming when they're new. For these chips, that was at least 22 years ago, back in 2002 for the 2114 and 2000 for the 2107.
The best you could do is to have someone find an old one in a cupboard that's been there for 20 years. This is the Coldfire Forum, so isn't the "right one" for finding those people. Search all forums for "MMC2114" and follow the similar questions starting from 2009 in "Legacy Codewarrior" ("support has been discontinued") and "Other NXP Products" (links to Lauterbach and other ones).
Being in the same family, the programmer you're using for the 2107 should be a starting point for programming the 2114. The interface (whatever it is) should be similar. One problem I can see is that the 2114 uses "Second generation FLASH for M•CORE", which is different to the previous one. So the code that generates the programming sequences is probably different.
The Lauterbach link (following the link that NXP Support provided in 2022) looks promising:
https://www.lauterbach.com/supported-platforms/chips/mmc2114/Essential-Debugger-with-USB#wizard-step...
Tom