Use Giemsa staining according to a malaria diagnostic.  Diff Quick staining will also work as a fast staining method. Try both and compare.

Although lysis of erythrocytes in a thick blood smear is something that is routinely done for malarial diagnosis, this is not appropriate for Babesia. Use a thin blood film. Air dry. As indicated by Usman, you do not want to lyse the erythrocytes, so do not heat and do not get any water (moisture) on the slide before fixation in 100% methanol (methyl alcohol). I fix for 1 to 2 minutes. If one fixes for too long, that might affect the uptake of stain, although I haven't actually tested this. So don't leave slides in the fixative and then go away and do something else. Do not use diluted methanol because that could result in lysis of red blood cells. I would use Giemsa's stain, as if you are trying to detect a malarial infection (as Patrick said). However, veterinarians tend to use quick-staining methods for Babesia, which makes sense under consulting room circumstances when owners of pets are there with their animals. First scan under low power, looking for "dots" inside erythrocytes. Then change to the X100 objective when you see something. It is not a good idea to start with X100 because then it will often take much longer (unless you are lucky) for you to find any babesial parasites that might be present.

May-Grünwald-Giemsa staining This is the commonly used staining of blood smears. Similarly, to other methods in histology it is based on the electrostatic interaction between dye and target molecules. The staining solutions contain methylene blue (a basic dye), related azures (also basic dyes) and eosin (an acid dye). The basic dyes carry net positive charges, consequently they stain nuclei (because of the negative charges of phosphate groups of DNA and RNA molecules), granules of basophil granulocytes and RNA molecules of the cytoplasm of white blood cells. The eosin carries net negative charge and stains red blood cells and granules of eosinophil granulocytes. It was originally thought that the granules of neutrophil granulocytes were stained by a „neutral dye” that formed when the above-mentioned dyes were combined, but the correct mechanism is not clear. The nuclei of white blood cells and the granules of basophil granulocytes appear in blue (staining with basic dyes), while red blood cells and eosinophil granules in red (because of red color of eosin). The cytoplasm of white blood cells are light blue, because of the low concentration of RNA molecules. Solutions: 1. May-Grünwald stain diluted with an equal volume of distilled water 2. Giemsa stain diluted with 9 volume of distilled water Procedure of staining: 1. Stain the fixed smears for 5 minutes in May-Grünwald stain diluted with an equal volume of distilled water! 2. Put the smears without washing for 30 minutes into Giemsa stain diluted with 9 volume of distilled water! 3. Wash the smears in distilled water and let them dry! 4. Observe the stained blood cells in light microscope! Results of the staining: The nuclei of white blood cells appear in blue, whereas the cytoplasm in light blue color. The cytoplasm of granulocytes contain some granules staining according to the type of the cell. The red blood cells appear in red. Look for different types of leucocytes! Draw them into the lab book!

We also used to use the stain referred to by Guy. I liked it. That was for blood parasites of birds. Then the need arose to compare in detail the morphology of our parasites with the appearance of parasites from birds that had been stained (by other people) with Giemsa. So I switched to Giemsa for inter alia avian hematozoa.

Thank You all for your  your help! Great  informative answers that  motivates me do more research on this microorganisms North American Malaria ( Babesia ) , Malaria and Boleria bogerferi, I will stick to Giemsa stain for Babesia parasites so I do not have to lyse the red blood cells as in malaria smear.

Of course, for malaria, you ideally need 2 smears. Both a thick smear and a thin smear. The red blood cells get lysed only in the thick smear. Use of the thick smear can result in faster diagnosis, as you might be aware. The thin smear is fixed before staining (the erythrocytes in the thin smear must NOT be lysed). This smear is used for determining the level of parasitaemia and species identification of malaria parasites present (should the patient indeed have malaria). If you use only one smear for malarial diagnosis, it must be a thin smear (no lysis of red blood cells). If you do not see parasites at first, continue to examine the thin smear (very thoroughly).