The /ɪə/ sound is spelled with <ear>, <eer> or <ir>.
There is a problem distinguishing /ɪə/ as a diphthong, acting as a syllable nucleus from an unstressed /ɪə/ making two syllables usually in a derivation such as cheekier from cheeky. Often the decision is borderline. Is sightseer two syllables or three? I have tried to limit the search to the first type. However, since this often carries stress, there were very few cases where it could be dropped. In some cases, such as peeress/press, it could be argued that there has been a shift of stress so the pair is not minimal.
The density value is irrelevant, since the base list of words containing the sequence of sounds /ɪə/ contains far too many non-diphthongal items.
buccaneer Buchan cashier cash charioteer chariot charioteers chariots earache rake eardrum drum eardrums drums earmark mark earmarks marks earphone phone earphones phones earpiece piece earpieces pieces earpiece peace earring ring earings rings earshot shot earwax wax earwig wig earwigs wigs emir M emirs M's endear end endears ends engineer engine engineers engines fakir fake fakirs fakes gadgeteer gadget gadgeteers gadgets marketeer market marketeers markets nadir neighed pamphleteer pamphlet pamphleteers pamphlets peeress press peeresses presses pierrot pro pierrots prose privateer private privateers privates profiteer profit profiteers profits racketeer racket racketeers rackets reindeer rained reindeer reigned reindeer reined sightseer sights sightseer sites steering string veneer Ven. vizier viz.
John Higgins, Shaftesbury, December 2010.