First answering the main part, cause it popped up in one of my games:
Q: Is there any way to increase the activation speed of a ring of invisibility to be anything but a standard action?
The reason here is the action economy balance. Assuming you can use your ring of invisibility with anything else than a standard action, you could use the standard to attack, then become invisible on the same round. Functionally, your Ring of Invisibility just becames a discount Ring of Greater Invisibility.
As a rule of thumb, activated magic items replicate something using a standard action. Allowing them to be used with anything less would allow people to, for instance, cast two (or more) spells per round, which is most of the time impossible1.
Supporting that, there are some items allowing you to quicken your casting2, but they only work a few times per day and are rather expensive. Moreover, they do not apply to activating magic items.
To any sane DM out there, asked if your player can quick/mmediate action activate their magic items that do not explicitly state it: bad idea. But hey, if you manage to immediately activate items, let me know, I have a wand of Fireball somewhere that became a lot more interesting.
Q: If not, is there anything that can apply a short burst of invisibility as a move or swift action?
A: I can't tell you with certainty there is not.
Some class features may cosmetically do that, but to the best extent of my knowledge, there is not. Cool spell such as Blink clearly state that even while being invisible 50% of the time, your opponents do not lose their DEX bonus to AC. The probability there is a way to do so is slim, cause the game designers have been extremely cautious about Sneak-attack like feature.3
However, you have more ways than Invisibility to trigger your roguish/slayerish features, and just asking a general way to do so, as Hey I Can Chan suggested might yield more results.
1: Except a few cases explicitly stated in the rules. Such exceptions including but not limiting to: Quickened Spell, immediate action spell such as Feather Fall, some Magus features if I recall.
2: Namely Metamagic Rods of Quicken Lesser/Greater.
3: Or, as some say on the forums: Rogues can't have nice things. I am personnaly of the opinion that there is a cabale of game designers bent on curbing my fun of one shotting encounters, but my friends say I'm raving. So, up to you to make your own opinion.