That very much depends on what you mean by "in game."

During a game?

Certainly:

PC: "I fall on my sword."
DM: "Okay. You die."

Using standard combat options?

No.

At least, not guaranteed at every table by a common understanding of the rules.

Coup de grace requires that the target be helpless before it's an option, and whether you're helpless to yourself is going to split the audience of DMs down the middle, more or less. Some will say no, you aren't helpless to yourself ("heck, people flinch away from their own razor!"), and others will say sure, go ahead and coup yourself out.

The combat actions and options made available by the game just aren't intended to cover every possible violence that a PC could commit. If you're alone, just you and a basket of puppies, and you pick it up and hurl it over the cliff, do you have to roll initiative? No — there's nobody there to contest with for the initiative. There's no action involved that's combative. At most it's a skill check, if for some reason there's the possibility of fumbling the throw and not disturbingly dispatching the puppies. It's not even a coup de grace.

When you're dealing with a character committing suicide (for whatever reason), unless it's suicide-by-battle the combat rules aren't engaged by the action. It's just violence, tragic or senseless, committed by the character against themself, vetted by the DM as possible and properly executed, and observed by your fellow players as a contribution to the shared imaginary space you're all consenting to create.

There are a lot of good options here; which, exactly are the best will depend on a lot of factors not specified.

Combat Reflexes has no prerequisites (though it's useless with Dex too low), and is pretty good for any melee character with decent Dexterity, and awesome for one with reach. A wild-shape druid will find reach not particularly hard to get, especially at high levels with big forms. These forms do tend to penalize Dexterity, so consider whether or not you'll still have enough Dex to put it to good use while in those forms. It also starts benefiting her right away if she is already melee-focused, but if she's starting as a caster-focus and planning to switch when she gets wild shape, then it'll be a dead feat for her for two levels.

Stand Still is another one that will be of a lot of use at higher levels, and probably not worthless even now. The main use for this is for a tanking type, to keeping enemies from just running right past you to attack the squishy allies you're trying to protect. It does have one prerequisite, Combat Reflexes, which I've already discussed above. If your Dex is high enough to already want CR, then this one will be a good buy as well. If not, this one's good, but not good enough to take CR just as a tax to get it, and its less good without CR's extra AoOs, anyway.

You mentioned Natural Spell, so she's apparently planning to still cast in combat, and as a druid, that means she's going to want to be using Summon Nature's Ally fairly regularly. For anyone summoning on a regular basis, Augment Summoning is awesome. It does cost two feats (Spell Focus (Conjuration) probably won't see much use from her), but its likely to be worth both of them. Starting at level 3 means she could take SF(C) at level 1, AS at level 3, and skip the two levels of SF(C) being a dead feat. This puts her in a very good position to be a summons-based controller/striker for two levels until wild shape comes into play, if she doesn't want to melee prior to getting that ability, and makes the same feats to support that, still be useful at higher levels.

If she's going to be casting in combat a lot, she'll probably also want to grab Combat Casting to increase the maximum level of spell that she can reliably cast defensively. There are equipment-based alternatives, but a lot fewer of them now that Pathfinder made concentration not a skill, and wild shape will get in the way of using most of the good ones.

Improved Initiative is very good for this character. As a wild-shape druid, her role in combat will be some combination of tank, striker, and/or controller, and all three of those, especially the controller, really want to go before any of the enemies do. I do consider II to be an overrated feat, but it really is quite good, just not as overwhelmingly good as the hype would have you believe.

Toughness is generally a rather poor feat, but being limited to core (less competition for those feat slots) and a druid focused on wild shape (eliminates usefulness of a lot of otherwise great feats) both make Toughness significantly less bad. Still probably not a top choice, but may be worth considering, especially if she's going for a tanking role.

Finally, Endurance and Diehard are pretty weak on their own, and even more so for someone who doesn't depend on heavy armor, but if you are considering adding non-core options later in the game, there are several really good ones for this character that need these as prerequisites.