You're being quite reasonable with a 2% target. Without substantial junk or going long (except for corporates and world hedged), it's not that hard to find solid bond funds with SEC yields at least that high. I've identified a reasonable representative for a number of different bond fund categories:
Corporate Bond (Lipper Corporate BBB): FCBFX (BBB, 7.79 year eff duration), 2.43% yield
Intermediate Core (Lipper Core): VCOBX (A, 6.04 duration), 2.02% yield
Intermediate Core (Lipper US Mortgage): OMBAX (BBB, 2.91 duration), 2.38% yield
Intermed Core Plus (Lipper Core Plus): BCOIX (A,
5.
56 duration), 2.28% yield
Intermed Gvmt (Lipper GNMA): PRGMX (AAA, 1.
50 duration), 2.63% yield
Short Term (Lipper Short Inv Grade): USSBX (BBB, 1.9
5 duration), 3.30% yield
Ultra Short (Lipper Ultra Short): TRBUX (BBB, 1.00 duration), 2.31% yield
World Bond (Lipper Global Inc.): DODLX (BBB, 3.20 duration),
3.62% yieldWorld Hedged (Lipper Global Inc.): FGBFX (AAA, 7.17 duration), 3.04% yield
ISTM there are four basic levers for bonds: credit rating/risk, duration, leverage, and options (more generally, derivatives). I've avoided leverage, tried to keep duration moderate to low, and credit rating above junk.
Options present not only a risk, but a risk in estimating the risk. Even for GNMA funds. Unlike vanilla bonds and vanilla funds, the effective duration shown for bonds with options are not exact calculations but are based on models that may fail at the worst times. These models make the effective durations shorter than for comparable vanilla bonds. In addition, the options (ability to pay off early or extend a mortgage past what a model predicts) tend to make the convexity close to zero or even negative. That means that when interest rates move, the effect on the prices of these bonds is worse than than on prices of vanilla bonds.
My point here is that one shouldn't just compare PRGMX to BCOIX and think the choice is a no brainer (higher rating, lower duration, higher yield). IMHO every fund above is worth a look depending on what one wants. But each one has a different risk profile (and a different amount of uncertainty in that risk). It's not just yield that matters, but total return and time frame.