I have a squier esprit, it's a low-end guitar, but it has the sweetest tone ever!
But the problem is, I'm having a hard time tuning it, also it doesn't hold the tuning for a long time.

So is there any guitar tuner with some presets? half-step down to be precise about what I need.

Anybody knows any?
Chromatic tuner. All the "presets" you could want, since it just tells you what pitch you're playing.

Oh, and new tuners (the ones on the headstock) and a new nut would probably help with your problem of it staying in tune.
yeah. go chromatic. but most guitar tuners even have the capabilities to read flat notes going down in half-step increments with the push of a button.
My Main Gear

gibson sg special faded
Fender Stratocaster (turning it into the black strat relic!)
cort stat 2t
ventura (ibanez artcore lawsuit era copy)
'74 alvarez acoustic

peavy transtube express 112