The first one of these was probably Jensen's model for the consistency of Suslin's Hypothesis (SH) with the Continuum Hypothesis (CH). This is by no means an easy model, e.g. it involves an iteration of length $\omega_2$ which is neither finite support nor countable support. Devlin and Johnsbråten wrote a monograph about it in the 70's titled The Souslin Problem (LNM 405).

There are better ways to do this nowadays. For example, Shelah has developed a variety of new forcings to kill Suslin trees and not add reals. These can be used to force CH + SH using a regular countable support iteration. In fact, because of advances in technology for preserving 'no new reals' there are probably lots more models of CH + $\lnot\diamondsuit$ out there.

As for general principles, the P-ideal dichotomy is compatible with CH but incompatible with $\diamondsuit$. There are probably lots more, but I'd have to check.

On the other hand, it is well known that it is very easy to inadvertently force $\diamondsuit$. For example, Rosłanowski and Shelah have shown that any proper forcing of size at most $2^{\aleph_0}$ that collapses $\aleph_2$ must force $\diamondsuit$ (and hence must collapse $2^{\aleph_0}$ too). Therefore, the only reliable way to force CH + $\lnot\diamondsuit$ via a countable support iteration proper forcing is to start with a model of CH and not add new reals.

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The first one of these was probably Jensen's model for the consistency of Suslin's Hypothesis (SH) with the Continuum Hypothesis (CH). This is by no means an easy model, e.g. it involves an iteration of length $\omega_2$ which is neither finite support nor countable support. Devlin and Johnsbråten wrote a monograph about it in the 70's titled The Souslin Problem (LNM 405).

There are better ways to do this nowadays. For example, Shelah has developed a variety of new forcings to kill Suslin trees and not add reals. These can be used to force CH + SH using a regular countable support iteration. In fact, because of advances in technology for preserving 'no new reals' there are probably lots more models of CH + $\lnot\diamondsuit$ out there.

As for general principles, the P-ideal dichotomy is compatible with CH but incompatible with $\diamondsuit$. There are probably lots more, but I'd have to check.

On the other hand, it is well known that it is very easy to inadvertently force $\diamondsuit$. For example, Rosłanowski and Shelah have shown that any proper forcing of size at most $2^{\aleph_0}$ that collapses $\aleph_2$ must force $\diamondsuit$ (and hence must collapse $2^{\aleph_0}$ too).