しゃ

The kokugos (apart from Nikk) only have 占者/せんしゃ. I think that should lead.

@@ -11 +11,2 @@
-<reb>うらないしゃ</reb>
+<reb>せんしゃ</reb>
+<re_restr>占者</re_restr>
@@ -18,2 +19 @@
-<reb>せんしゃ</reb>
-<re_restr>占者</re_restr>
+<reb>うらないしゃ</reb>

占い師	1701994	97.9%
占師	27819	1.6%

占者	8292	0.5%
占い者	903	0.1%


Main dictionary with the picture & everything is under うらないしゃ. Second defn is  せん‐しゃ【占者】, 〘名〙 (「せんじゃ」とも)
https://kotobank.jp/word/占者-550066
精選版 日本国語大辞典 「占者」の意味・読み・例文・類語
うらない‐しゃ うらなひ‥【占者】

Example of  占者 = うらないしゃ
https://japanknowledge.com/articles/hmrkns/kns004.html   (as furigana on a definiton)
https://9rakugo-fan.seesaa.net/article/201808article_2.html  今回採り上げるのは易者（占者うらないしゃ）である。
占者 = せんじゃ
https://sarumeigaku.com/sarukoblog/archives/18544
https://namboku.jp/?page_id=266   その本数によって占者（せんじゃ）

占者 doesn't even have せんしゃ or せんじゃ (few examples though)
https://furigana.info/w/占者
うらないしゃ	33.3%
うらなひしや	33.3%
うらない	26.7%
せんせい	6.7%


yourei examples of 占い者 (plentiful, 53 examples)
https://yourei.jp/占い者

yourei for 占者(90 examples). rare furigana, but where it appears, it's about 2-to-1 for うらないしゃ over せんじゃ.  せんしゃ never appears.
https://yourei.jp/占者

Can't speak to historical usage, but modern use seems to clearly prefer せんじゃ over せんしゃ (the latter being nonexistent, even though the old kokugos seem to feel differently). 

うらないしゃ needs the full 占い者 form.  It really feels like うらないしゃ should come first as a reading, even though daijs doesn't give it explicitly.  This is probably one of those [col]/[form] kunyomi/onyomi splits we've put into one entry.

Just searching for "占者" alone, this is what I encountered(せんじゃ):

Manga called 占者高生 星見先輩． Reading: せんじゃこうせい ほしみせんぱい
https://mangapedia.com/占者高生星見先輩-qbkwratb9

Fortune-teller playing card:
未来占者　＝ みらいせんじゃ
https://www.cardrush.jp/product/51747
Another:
探検隊の占者 たんけんたいのせんじゃ
https://mtg-jp.com/products/card-gallery/0000192/491685/

うらないじゃ(ja) was noted previously as only in nikk.  That would be a very unusual pronunciation (there are 0 other occurrences of verb-form-い者 as じゃ, and only a few nouns that end in いじゃ.  At best, most likely archaic.  For me, this falls into the "more harm than good" category to be visible.　There might be some book results from the 1800s, or I'd just drop it entirely.

Windows 11 IME cannot complete any of these but うらないしゃ.

ngram counts for furigana forms are useless for determining frequency, because せんしゃ and せんじゃ have more common, unrelated uses (戦車, 選者). The terms are too rare to search ngrams with disambiguating collocations.

@@ -7,6 +7,3 @@
-<r_ele>
-<reb>せんしゃ</reb>
-</r_ele>
-<r_ele>
-<reb>せんじゃ</reb>
-</r_ele>
+<k_ele>
+<keb>占い者</keb>
+</k_ele>
@@ -16,0 +14,8 @@
+<reb>せんじゃ</reb>
+<re_restr>占者</re_restr>
+</r_ele>
+<r_ele>
+<reb>せんしゃ</reb>
+<re_restr>占者</re_restr>
+</r_ele>
+<r_ele>
@@ -17,0 +23 @@
+<re_inf>&sk;</re_inf>
@@ -20,0 +27 @@
+<xref type="see" seq="1588460">占い師</xref>

I think "palmist" is too specific.

@@ -20,0 +21 @@
+<gloss>fortune teller</gloss>
@@ -22 +22,0 @@
-<gloss>fortuneteller</gloss>
@@ -24 +23,0 @@
-<gloss>palmist</gloss>

Interesting.