While drafting a new constitution, the Cabinet refused to sign it, even though two thirds of the native Hawaiians were supporting it. The fear of bloodshed made her surrender. When the Queen would have gathered the forces of the people and not give up her throne and let the Committee of Safety overthrow the monarchy, would the Kingdom have survived?
Welcome to History SE, Helena!
Once the coup began, it's unlikely Queen Liliʻuokalani could have done much of anything to preserve the monarchy, or restore it once the provincial government was established.
Hypothetically, even if we set aside the fact that the Queen was thoroughly opposed to engaging in armed hostilities, in the long run it's still highly unlikely events would not have ended up essentially the way they did. Simply put, she had neither the time to respond nor the manpower to do so.
Until the day before the coup (January 16), the Queen and her advisers thought the only realistic danger might come in the form of mob violence by the common citizen. This is why she made a statement on January 16 assuring her subjects that she would only seek to alter the existing constitution under means already prescribed within it, rather than proclaim an entirely new constitution. Once she made this announcement, the threat of imminent mob violence was seemingly averted.
Later that same day, the coup plot was actually discovered before it began. Yet despite this, the Queen's cabinet forbade the arrest of the Committee of Safety because of their US associations. Regarding this:
"[The cabinet] had been in office less than a week, and whatever they thought about the need for a new constitution... they knew enough about the temper of the queen's opponents to realize that they would endure the chance to challenge her, and no minister of the crown could look forward... to that confrontation".
(I don't have access to the original source of this quote at this time, but I was able to find another reference to it here. Apologizes if there's any errors, as I couldn't double-check against the original.)
Essentially, the coup was knowingly allowed to happen. I won't speculate here, but it's interesting to consider the cabinet's response to a known, impending coup attempt.
When the coup did occur on the 17th, the Queen had at her disposal roughly 500 men (comprised of the Royal Guard, police, and other volunteers), whereas her opponents numbered upwards of 1,500 armed Hawaiian subjects(*). She was outnumbered three to one. Afterwards, once the Queen's opponents were entrenched in their newly formed provisional government backed by the United States, there was no realistic way for her to assemble a resistance force capable of opposing the US Marine and Naval forces present.
But, again, this is all just a thought experiment. For the Queen to have organized a combative force would have been antithetical to her goals. Queen Liliʻuokalani repeatedly stated her firm intention to avoid any bloodshed whatsoever during these events, and until her death held out hope that she would find a diplomatic path to restore her position.
* (Additionally, the Queen perceived the roughly 160 US military personnel that were brought ashore shortly before the coup began as being part of the coup forces, although in reality they were ordered to maintain neutrality. Either way, her forces were still heavily outnumbered.)