Hamilton makes a variety of microliter syringes (
https://www.hamiltoncompany.com/products/syringes-and-needles/general-syringes/gastight-syringes ). It has been a few decades since I looked seriously at its offerings. All of them use a hollow-bore needle, and that might not be the easiest to control with a paste. Besides, 1 uL = 1 mm^3, which is quite a bit.
For sub-microliter amounts, I use homemade needles made from various sizes of music wire. You can also buy assortments of fine needles that are made to oil watches. They are usually flattened, so application might be easier. Delivery amounts are calibrated for oil. Dispensing 0.1 uL and smaller is easy to do.
My thinking was that if the pitch were 0.5 mm or larger (preferably 0.65 mm or more), I would just hand solder rather than go through the trials, tribulations, and cost of learning a reflow technique using a hot plate. Temperature regulated hot air, as suggested by Diver300, might be easier. But still, the equipment cost for one off or even 10 off might not be justified.