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The word 弓形 has three different readings which are きゅうけい, ゆみがた, and ゆみなり. Unfortunately, there does not seem to be much distinction between these three readings. Is this simply a case wherein all readings are acceptable or is one reading more common than the others?

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The kun-reading ゆみがた is the safest reading at least in ordinary speech and writings.

弓形 may be read きゅうけい in some technical fields I'm not good at, but I can say it's rare. In mathematical contexts, this word is normally called ゆみがた (see this video and this Wikipedia article for example), not きゅうけい. I guess this is because there is a more common word with the same reading, 球形 ("spherical").

ゆみなり is a common word, but it's usually written as 弓なり in modern Japanese.

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