V --> VgV for all vowels.
e.g. in Spanish:
   <bueno tiempo> --> <bueguenogo tieguempogo>, I presume.
(Writing just as a Spanish native speaker not as phonetist that i'm just amateur) I think that i would transform in that way:
    buen tiempo ---> bugueguen tiguiegempogo /buguegen tigiegempogo/
The components in diptongs are treated independently each one. 
In another example:
    rosa y azul --> rogosaga igi agazugul
Would happen that althought < y > between vowels has the pronuntiation as a consonant, that is the [j] (with an up-down circunflex instead of the point), it would be understood as a vowel sound. But, in Spanish also, if the following word starts with /i/ then the conjunction < y > use to change to /e/, < e >, as for example in:
   bonito e interesante
So that allophony for this particular word -the copulative conjunction- is quite extreem and part explicit. The disyunctive conjunction also has explicit allophony, as it is /o/ but becomes /u/ if it's followed by /o/.
Now, what's interesting here is that the Polish nasal vowels spelt <a,> and <e,> (with a cedilla-like diacritic) -- often described as nasal [o~] and nasal [e~], but actually realised as diphthongs (in which the second element may be analysed as an allophonic variant of a nasal consonant) -- become -ogoN-/-egeN- rather than -oNgoN-/-eNgeN-. This supports a biphonemic /VN/ interpretation of Polish nasal vowels.
The game also sheds some light on the phonemic status of the Polish vowels spelt <i> (pronounced [i]) and <y> (a high central vowel), which are in more-or-less complementary distribution. The fact that -i- is transformed into -igi- and -y- into -ygy- (though -gy- does not normally occur in Polish) suggests that speakers treat these sounds as distinct phonemes.
My question is: are there any traditional ludlings in your native languages? and if so, are there any interesting phonological phenomena involved in their production?
I only remember one consisting in the substitution in a short verse of all vowels for the same vowel, first all becoming /a/, then, succesively all becoming /e/, then /i/, then /o/ and the /u/. But i don't see any interesting phonological phenomena apart that the game itself shows how conscious are Spanish speakers of their vocalic phonems.