How do sefardim pronounce the tzerei? Is it "eh" as in elephant or "ay" as in play?
A little phonetics background is needed to answer this question. Phoneticians usually transcribe sounds in languages using a set of symbols known as the International Phonetic Alphabet (IPA). Phonetic transcriptions in the IPA are written in between square brackets , so for example the word "beds" is transcribed in IPA as [bɛdz].
As you can see from the previous example, the "eh" sound is written in IPA as [ɛ]. It's also useful to know that the "y" sound is written in IPA as [j], so for example the word "yes" is transcribed as [jɛs].
Now what about the vowel sound in the word "plays"? Well, if you think about it, the shape of your mouth changes as you pronounce the "ay" vowel in this word -- over time, it constricts more and becomes closer to the sound [j]. However, there are languages (e.g. French) which have a vowel sound similar to "ay" but more "pure", in that the shape of the mouth doesn't change over time -- this sound is written [e] in the IPA, and you can listen to a recording of it here. For example, the French word "été" is pronounced [ete] with a "pure" "ay" sound for both vowels. By contrast, the English word "plays" is pronounced as [plejz], where the vowel starts as an [e] vowel but shifts to a [j] over a short period of time. (This is what is known as a diphthong.)
Now, there are also languages that have a vowel that is intermediate between the vowels [ɛ] and [e]; this is sometimes written as [e̞]. For example, Modern Hebrew uses the vowel [e̞] for both tzere and segol. For more information on these three vowels, and to listen to recordings of them being pronounced, see the Wikipedia articles on [ɛ], [e], and [e̞].
Two other vowel sounds that we will need to know: The vowel in the English word "bit" is written as [ɪ] and the vowel sound in the English word "beet" is written as [i], so these two words are transcribed as [bɪt] and [bit], respectively. For more information and recordings, see the Wikipedia articles on [ɪ] and [i].
Now that we understand the phonetics behind these vowels, we can understand their realizations in Sephardic Hebrew. The following quote is from S. Morag, "Pronunciations of Hebrew", Encyclopaedia Judaica XII:
ṢERE AND SEGOL
All the communities which follow the Sephardi pronunciation have one realization for both ṣere and segol (see above). This realization is a front higher-mid or lower-mid vowel, [e] or [ε]. In some North African communities no distinction is made between the realizations of ṣere (and segol) and that of ḥireq. This applies also, to some extent, to the Iraqi community.
So according to Morag, both segol and tzeirei are pronounced identically in the Sephardic pronunciation, and depending on the variety of Sephardic Hebrew are both pronounced as [ɛ], [e], or [e̞]. My own speculation is that this depends on whether the local language of the area those Jews lived in used [ɛ], [e], or [e̞], and that there has been a shift to [e̞] among Sephardic Jews living in Israel due to the influence of Israeli Hebrew. Also, when Morag refers to some communities that merge tzere/segol and hiriq, I infer that the pronunciation of this merged vowel is [ɪ] or [i] – as you can hear in this recording of Adon Olam sung in Tunisian Hebrew.
In summary, the possible Sephardic pronunciations of tzere are [ɛ], [e], [e̞], and [ɪ] or [i]. A caveat: These vowel sounds are not really discrete categories; rather, there is a continuum of vowel sounds stretching from [ɛ] to [i], and the separation into five categories is something of a convenient fiction.