Anyway, to answer my own suggestion now that I'm back home, here's how dieu+pater goes to Iuppiter:
So you start with two PIE words: diēu- and pater. Both are athematic. An ablauting form of diēu-, dieu forms the antecedent of what would come to be "Jupiter" namely: dieupater. One phonological change visible in all PIE languages is the "alternation of /i - j/ and /u - w/". Which is to say that, in the context of this word, an unstressed /i/ becomes a /j/ (English y like in youth) and a /u/ becomes the approximate /w/ when preceding a vowel. *dieu+pater was one such recipient of this change, and consequently became *djeupater. The next change, occurring perhaps some time around 500 BC was part of the "Changes in certain consonants followed by /j/ (C+j changes). The one relevant to this example being that in /dj, gj, sj/ , the initial consonant dropped out resulting in simply /j/, so thereby *djeupater -> jeupater; Italic stress occurring around the same time moved the variable stressing of PIE to stress always occurring on the vowel in the initial syllable, so jeupater -> jéupater. Around 300 BC Latin underwent changes to short vowels in unstressed syllables. This change is reflected, for example, in a number of compound verbs, e.g. facio raising to ficio when a prefix is added (i.e. the ordinarily stressed a becoming unstressed due to the presence of a prefix like prae or inter). In terms of relevance to Juppiter these are:
1) a -> e when /a/ is unstressed and followed by at least one syllable
2) e -> i when followed by one consonant and one vowel when the consonant is not /r/ AND when the preceding sound is not /i/ or /j/.
So in the case of *jéupater, the unstressed a, followed by the syllable "-ter" became *jéupeter, and thence, the unstressed e, followed by non-r becomes *jéupiter
So *jéupater -> *jéupiter. From there at around 250 BC Latin underwent another change in which /e/ -> /o/ when followed by a w or u, so *jéupiter -> *jóupiter. Around 200 BC the diphthongs /ei/ and /ou/ underwent changes. In this example: /ou/ became /ō/ if it preceded an /n/ or a /t/, else it became a /ū/. You can also see this, for example prówtens -> próudens -> prūdēns. So following these changes:
*jóupiter -> Jūpiter which is our first form that is actually attested in Latin. From there in some cases, a stressed long vowel followed by a consonant sporadically would unlengthen the vowel and make the consonant geminate. This was not uniform and occurred between 100 BC and 1 BC (i.e. during the "Classical Latin" period). So Jūpiter -> Juppiter.
The vast majority of this is taken from Joseph Voyles and Charles Barrack, An Introduction to Proto-Indo-European and the Early Indo-European Languages (Slavica, 2009), specifically page 163 for the theoretic iterations of Juppiter, with other assorted pages for specific explanations of the phonological rules.