First and foremost you must ask yourself about the focus of your work. Is it related to the age of sedimentation, diagenetic or hydrothermal overprinting, and age of erosion and source rocks and secondly what age interval may I expect. There is a wide range of radiometric dating methods involving U/Pb, Rb/Sr, Sm/Nd, K/Ar, Ar/Ar or in younger formations, e.g., C and Be. All of them make only sense as they are applied to in-situ mineralizations. So they do not really describe the process of sedimentation but stage 2, diagenesis and hydrothermal alteration. Only the youngest processes address the process of sedimentation. Other methods are based on biological processes like dendrochronology or they make use of lichen or the magnetic features of a sedimentary unit. There is a prerequisite which needs to be fulfilled in every case. You have to carefully study the geology and mineralogy first so as to know what the relative age relation is like among the various constituents.
As I understood you have clastic rocks. The clastic rocks have mineral constituents derived from more than one source, each mineral gives the age of its source rock " assuming a state or radioactive secular equilibrium exists". So, it is impossible to have a true age dating for clastic rocks by simple method of dating as we do for hard rocks. You will then have mixed ages. You can use 87Sr/86Sr stratigraphy if you have chemically formed sediments such as limestone but since you have clastic sediments you will have minerals with different 87Sr/86Sr ratios. People try to use Thermoluminescence dating (TL dating) for clastics and age of sedimentation but with high uncertainty.
TL dating is the determination, by means of measuring the accumulated radiation dose, of the time elapsed since material containing minerals was either heated (lava, ceramics) or exposed to sunlight (sediments).
It is possible to determine the age of non-fossil destructive rocks with the help of the age of the upper and lower stone layers, and the age of the newest fragments in the rock.
Luminescence dating, optically stimulated luminescence (OSL) could be a possible method. Check the follwing references:
1- Evangelos Tsakalos et al., 2018. "Testing optically stimulated luminescence dating on sand-sized quartz of deltaic deposits from the Sperchios delta plain, central Greece".
2- Athanassas and Wagner, 2016, "Geochronology Beyond Radiocarbon: Optically Stimulated Luminescence Dating of Palaeoenvironments and Archaeological Sites"
Luminescence dating has many novel applications because it can utilize the most ubiquitous minerals in the Earth’s crust (quartz and feldspar) to determine the timing of sediment burial or exposure. The technique can be applied to grain sizes from silt to boulder, and to sediments that occur in a wide range of settings, e.g. deserts, rivers, lakes, glaciers, caves. This issue discusses the latest technical developments of luminescence dating and the key scientific discoveries that it has facilitated over the last few decades
I think U-Pb in zircón with LA-ICPMS because you can have the maximum sedimentation age! and with the old cores you can have the age of the different source.
Dating method that estimates the amount of light energy stored in rocks known as Luminescence dating employing thermoluminescence and optically stimulated luminescence) can be used in derived soils to obtain an absolute date for a specific event that occurred in the past.
Unfortunately, it would be a tough question if you mean the sedimentary age. However, Re-Os chronology and chemostratigraphy could be a choice if you have abundant organic matter in your clastic rocks. See example from Xu et al., 2017 Nat Geoscience dating a Toarcian lacustrine shale by Re-Os system.