Man, visit Nashville sometime. Those guys/gals are pros at getting tips without being jerks about it.
I think there's no problem at all with asking for them. Why have it if you're not gonna mention it?
Either that or make the jar much more obvious. Perhaps lime green and hit it with a black light.
This.
It's probably tacky if there's a cover charge (though this is probably arguable). However, whether you're getting paid or not by the venue doesn't mean anything. It's not the audiences business. We put a tip jar out and put one of those mini strings of LED's inside it.
With the piss-poor rates that most bars are willing to pay there's no reason not to have a tip jar and work that jar hard.
Helps to have a schtick too. My singer calls me "Goose" (like the guy in Top Gun.) and about once a set he takes up a collection for "Gooses' Goslings". He asks me how many kids I've got and I hold up my hand. First set it's 4.
"4 kids all in diapers folks, let's help Goose get some Formula and Diapers"
Then second set he asks again and it's 5 kids. Hilarity ensues, people laugh, singer adds condoms to the list of things they can help me buy with their generous tips.
Sometimes in set 3 I have 6 kids....
No one will know or care that you have a jar unless you work it.
Other tips/tidbits:
-If you've mentioned the tip jar, folks will put money in it when the request their favorite artist or song. Even if you don't know it specifically, you can usually repay their tip by playing one of their other favorite artists.
-Letting someone sing a song or two is a great way to get some more tips.
-Having an enthusiastic female fan take the tip jar around the bar helps.
ADDENDUM.
I should add that all of what's above comes from my time in a band playing covers, mostly in bars, restaurants, etc. When I was in an original band, playing mostly places that have a cover, we almost never put out the tip jar. For a special/corporate/wedding/private event I'd also likely not put out a tip jar.